Author's authorized chapter previews. Sections 1.7, 1.8 and 1.10 develop invariant probability distributions, convergence to equilibrium and the countable-state Markov chain ergodic theorem for Markov chains. The distinction between a normalizable invariant measure and an invariant measure of infinite mass is crucial on a countably infinite state space.
Handbook Section 1.3.5.3 distinguishes paired from unpaired observations and equal-variance from unequal-variance inference.
Handbook Section 7.4.3.2 specifies the model and assumptions on its errors.
Handbook Section 3.2.3.1 explains the one-factor layout and within- versus between-level variation.
The NIST/SEMATECH e-Handbook of Statistical Methods explains score-based binomial proportion confidence intervals and gives the Wilson score interval endpoints.
Publication details and the original axioms are discussed in The Sources of Kolmogorov’s Grundbegriffe by Glenn Shafer and others.
Cited passages: slides 6-10 and 17-18.
Cited passages: 1.4-1.6, especially consequence C9.
6.438 Algorithms For Inference, Fall 2014, recitation notes; institutional authorship.
Cited passages: §1, The Junction Tree Algorithm; §6, Relationship between chordal graphs and junction trees.
Cited passages: introduction, page 70; section 5.1.1, page 87.
Publisher: MIT OpenCourseWare (host of the author’s draft).
Cited passages: Chapter 2, section 2.2.4, printed pp. 78-79: counting-process definition and its equivalence to exponential interarrival times.
Publisher: Cambridge University Press.
Cited passages: Section 7.1, Theorem 7.2, printed p. 59: interval theorem characterizing independent exponential gaps; Sections 5.2-5.3, Definition 5.7, Proposition 5.5, Theorem 5.8 and Corollary 5.9, printed pp. 42-44: location-dependent independent marking, intensities, and independence of the split processes.
Publisher: National Institute of Standards and Technology.
Section 1.3.6.6.11, Gamma Distribution: www.itl.nist.gov/div898/handbook/eda/section3/eda366b.htm gives density, shape/scale conventions and the gamma-function integral. Section 1.3.6.6.9, Lognormal Distribution: www.itl.nist.gov/div898/handbook/eda/section3/eda3669.htm defines the logarithmic-normal parameterization and gives mean, standard deviation and coefficient of variation. These conventions support the original inverse-moment derivations in the thickness-model article.
Section 7.2.4.1, Confidence intervals: www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm . The subsections One-sided confidence intervals and Exact Intervals for Small Numbers of Failures explain one-sided limits and binomial-tail inversion. Inverting the extreme probabilities gives an upper event-probability bound one minus alpha raised to the power one over n for zero events, and a lower detection-probability bound beta raised to the power one over m for all-success calibration. The joint-coverage and rare-event examples are original derivations, not NIST experimental data.
Section 7.4.7.3, Bonferroni’s method, www.itl.nist.gov/div898/handbook/prc/section4/prc473.htm : simultaneously valid statements are obtained by dividing the allowed error probability among comparisons. This supplies the finite-candidate coverage principle used in the confidence-allocation article; the uniform-location counterexample there is an original construction.
Section of NIST and SEMATECH e-Handbook of Statistical Methods. The construction of a central composite design uses a full or resolution V factorial design; Table 3.22 compares circumscribed, inscribed and face-centered variants.
Section of NIST and SEMATECH e-Handbook of Statistical Methods, issued and hosted by the National Institute of Standards and Technology. No individual section author or section publication or revision date is established.
Inspected locators: confidence interval formula; interpretation of confidence intervals; normality assumption and population mean discussion.
Section of NIST and SEMATECH e-Handbook of Statistical Methods, issued and hosted by the National Institute of Standards and Technology. No individual section byline or publication or revision date is established.
Inspected locators: Probability Density Function; Cauchy special case and normal limit; Common Statistics. The inspected page presents integer degrees of freedom.
Section of NIST and SEMATECH e-Handbook of Statistical Methods, issued and hosted by the National Institute of Standards and Technology. No individual section byline or publication or revision date is established.
Cited passages: Section 1.3.5.16, Characteristics and Limitations, items 1 and 3; Definition; Section 1.3.5.16, Critical Values: alternative scalings must match the statistic; Section 1.3.5.16, Definition and Technical Note: the formula must include both i/n and (i-1)/n.
Cited passages: §1.3.5.11, Alternative Definition of Kurtosis, normal baseline and software convention warning.
Institutional handbook section issued by NIST and SEMATECH; no individual byline or section date is established.
Cited passages: §8.2.2.1, a) Exponential Model; Data points line up roughly on a straight line when the model chosen is reasonable.
Publisher: R Project documentation, hosted by ETH Zurich.
Cited passages: Details, numeric second sample and two-sample ties; Source, exact and randomization distributions; Details: one-sample ties and rounding; numeric second sample; final paragraph on prespecified parameters.
Publisher: Taylor & Francis (current publisher platform).
Published in Journal of the American Statistical Association, volume 62, issue 318, pp. 399-402.
Cited passages: Printed pp. 399-400: opening procedure and Table 1 of the original article; inspected mirrored text.
Collection of sources; individual chapter authors and dates are recorded below.
Cited passages: Modern regression 1: Ridge regression, slide 7: center predictors, leave the intercept free and scale predictors to sample variance one; Modern regression 1: Ridge regression, slides 5 and 7: summed squared-error objective and unpenalized intercept.
Cited passages: Model selection and validation 1: Cross-validation, slides 5–8 and 11–14: tuning for prediction, training error and refitting on each training fold; Model selection and validation 1: Cross-validation, slides 6–8 and 11–14: fresh-response error, training error and held-out scoring.
Cited passages: Regression 1: Different perspectives, slides 6–10: fitted values, hat matrix, projection and orthogonal residuals.
Collection of sources; individual chapter authors and dates are recorded below.
Cited passages: High-Dimensional Regression: Ridge, section 1, p. 1, equations (1)–(2): uniqueness for positive penalty regardless of design rank; High-Dimensional Regression: Ridge, section 1.1, pp. 1–2: shrinkage of fitted principal-component directions.
Published in Journal of Machine Learning Research, 11(70):2079–2107.
Cited passages: On Over-fitting in Model Selection and Subsequent Selection Bias in Performance Evaluation, introduction, pp. 2079–2080: selection as part of fitting and nested assessment.
Collection of sources; individual chapter authors and dates are recorded below.
Publisher: Stanford University (official CS229 hosting).
Cited passages: Duchi, CS229 supplemental notes, §3, p. 6, lemma 5: all-real-parameter moment-generating function bound; John Duchi, CS229 supplemental notes, §3, p. 6, theorem 4: independent bounded variables and both tails.
Published in Journal of the American Statistical Association, volume 58, issue 301, pp. 13–30.
By Scott Sheffield, as credited on the PDF title slide. No date is assigned from the URL alone.
Cited passages: PDF pp. 4–8 define conditional expectation and its uniqueness up to almost surely equality; pp. 9–11 discuss integrability and uniqueness.
By Rick Durrett. The author-hosted PDF title page identifies Version 5, January 11, 2019; the preface describes the fifth edition.
Cited passages: Probability: Theory and Examples (fifth edition), PDF title page (PDF p. 1): title, whole-book author, Version 5 January 11, 2019, and copyright; Preface (PDF p. 3): fifth edition identification; §2.5 Convergence of Random Series, printed p. 81 (PDF p. 89): tail sigma-field definition and Examples 2.5.1–2.5.2; Theorem 2.5.3 and proof steps (a)–(b), printed pp. 81–82 (PDF pp. 89–90).
Additional cited passages: §3.3.1 definition, printed p. 125; Theorem 3.3.1(a)–(d) and proof, and Theorem 3.3.2 and proof, printed p. 126; §3.3.3, Theorem 3.3.18, printed p. 134.
Cited passages: the definition starts on printed p. 205. Equation (4.1.5) and Theorem 4.1.13 on p. 212 give the law of total expectation and nested tower property. Theorem 4.1.15 on p. 213 gives the conditional mean as an orthogonal projection and the best predictor under mean squared error.
Published in the Journal of the American Statistical Association, volume 102, number 477, pp. 359–378.
Cited passages: §1, printed pp. 359–360: reward conventions and optimum-score estimation; §3.1, Example 3, printed p. 363: logarithmic score, relative-entropy argument order and the historical reference to Good (1952); §4.1: density scoring rules.
Published in the Journal of the Royal Statistical Society, Series B, volume 14, number 1, pp. 107–114.
Cited passage: the published summary describes encouraging accurate probability estimates and a connection with information theory.
Publisher: Kappa Research LLC.
The linked §3.1.5 discusses special discrete distributions. The book citation gives Kappa Research LLC, 2014; no section revision date is asserted.
The linked §1.3.1 introduces random experiments, outcomes and events. The year 2014 belongs to the existing whole-book citation, rather than a section revision.
Cited passages: Section 6.2.1, equation (6.2) and the closing paragraph on the expected number of occurring events.
By David A. Levin and Yuval Peres, with contributions by Elizabeth L. Wilmer.
Publisher record: doi.org/10.1090/mbk/107
Cited passages: §4.1, Proposition 4.2 and Remark 4.3, printed p. 48: finite-state discrepancy formula; §4.2, Example 4.6, Proposition 4.7 and equation (4.13), printed pp. 49–52: coupling and common-mass construction. The author-hosted second-edition PDF text and title page were inspected; the numerical examples here are original.
Publication metadata: American Mathematical Society, 2017; hardcover ISBN 978-1-4704-2962-1, as listed in the publisher's [ref].
Collection of sources; individual chapter authors and dates are recorded below.
Publisher: Springer, Berlin, Heidelberg.
Cited passages: Section 2.1, Definitions 2.1-2.2, printed pp. 26-27: expected counts and intensity functions; Section 2.1, Example 2.3, printed pp. 26-27: randomly translated grids have constant intensity.
By Herman Chernoff, credited as H. Chernoff in the institutional catalogue.
Repository identifier: purl.stanford.edu/sw496fn0032
The Stanford Statistics record gives report number SOL ONR 6 and report date November 1951. The catalogue metadata was inspected; the report's full text was not accessible during this pass. The record is cited for historical authorship and date, not as an inspected proof passage.
Publisher: The MIT Press.
Chapter 2, Regression, §2.3, (2.23)–(2.24), (2.38), (2.42): gaussianprocess.org/gpml/chapters/RW2.pdf
Published in Statistics 154, Spring 2025.
Publisher: University of California, Berkeley.
Published in Foundations and Trends in Communications and Information Theory 1(4), pp. 417–528, by now Publishers.
Published in The Annals of Probability 3(1), pp. 146–158, February 1975, by the Institute of Mathematical Statistics.
Published in Physical Review, volume 36, issue 5, starting p. 823.
Cited passages: On the Theory of the Brownian Motion, abstract: velocity minus its decaying initial contribution; friction coefficient divided by mass.
Publisher: Cambridge University Press.
Cited passages: Applied Stochastic Differential Equations, Example 6.2, printed p. 81, equations (6.27)–(6.30); centered model with diffusion constant q; Applied Stochastic Differential Equations, Example 6.8, printed pp. 91–92, equations (6.73)–(6.76): steady-state variance and covariance.
Cited passages: §2, Terminology, definition of κ; §4, counterexamples with different peaks; §5, central and tail contributions; §5, Why Tails Mostly Determine Kurtosis, inequality (1) and following fixed-h argument.
The notes homepage gives a last-updated date of 1 May 2024.
Cited passages: §4.3, Problem 4.10 and its solution; §4.3, Problem 4.8 and its solution.
Publisher: Taylor & Francis on behalf of the American Statistical Association (mirror wrapper metadata).
Published in Journal of the American Statistical Association, volume 69, number 346, pp. 383-393.
Cited passages: Frank R. Hampel, The Influence Curve and Its Role in Robust Estimation, p. 383, §2: pointwise right-limit definition along mixtures with a point mass; Frank R. Hampel, The Influence Curve and Its Role in Robust Estimation, §4, p. 386: exact asymptotic curve supplemented by behavior at other distributions, especially empirical ones.
Publisher: Institute of Mathematical Statistics.
Published in The Annals of Mathematical Statistics, volume 35, number 1, pp. 73-101.
Cited passages: Peter J. Huber, Robust Estimation of a Location Parameter, §11, pp. 95-96: estimating location when normal-component scale and contamination fraction are unknown; Peter J. Huber, Robust Estimation of a Location Parameter, §3, p. 78: derivative normalization; §4(iii), p. 79: clipped location criterion and central-mass denominator.
Cited passages: original journal wrapper and byline, March 1964 publication; §1, printed pp. 73–75; §2, printed p. 76, minimizing set; §4(iii), printed p. 79, piecewise criterion and clipping about the fitted location. The manuscript receipt date, 4 June 1963, precedes publication.
Archived chapter draft dated 1 April 2015. This timestamp identifies the inspected draft, not a print publication date. The parent is an author-hosted draft textbook, not a claim that Cambridge University Press published this version.
Cited passages: §21.1.3, printed p. 443, equations (21.2)-(21.3), and §21.1.7, p. 446: choose a label, then sample its component; §21.1.5, printed pp. 444-445: observational equivalence and label degeneracy; §21.1.6, printed pp. 445-446: probabilistic clustering and evaluation on future data.
Publisher: Stan Project.
This source is credited to an organization.
Version2.37, Regression Models, Hierarchical priors: hyperpriors on the parameters of lower-level prior distributions.
Cited passages: Finite Mixtures, section Recovering posterior mixture proportions: Bayes formula for label probabilities conditional on the observation, component parameters, and mixing weights; Finite Mixtures, sections Latent discrete parameterization and Summing out the responsibility parameter: nonnegative normalized weights, categorical labels, and the sum of weighted normal densities.
Explicitly authored standalone online lecture. Fall 2025 identifies the course offering, not a separately verified publication or revision date.
Cited passages: Sufficiency, Will Fithian, “Factorization theorem”: common dominating measure and almost-everywhere factorization; Sufficiency, Will Fithian, “Independent Bernoulli sequence”: conditional pmf; Sufficiency, Will Fithian, “Sufficiency”: definition.
Publisher of the underlying book: American Mathematical Society.
The linked CHANCE Project version is dated 4 July 2006. Its cover identifies the underlying second-edition book as copyright 2003 by the two authors, and this version as copyright 2006 by Peter G. Doyle. The version credit does not identify Doyle as an original-book coauthor or formal editor. These dates describe copyrights and a version, rather than a claim about first publication.
Cited passages: §3.1, Example 3.3 and Table 3.1, printed pp. 77–78: uniform-calendar assumptions, distinct-label product and threshold.
Section 6.1, Definition 6.1, printed p. 226, defines finite discrete expectation by summing values weighted by their probabilities. This is the discrete calculation used in nonnegative random variable. Online text: math.dartmouth.edu/~prob/prob/prob.pdf .
Published in Journal of the Royal Statistical Society. Series B (Methodological), volume 39, number 1.
Joint article by Arthur Pentland Dempster, Nan M. Laird and Donald B. Rubin, printed with the byline A. P. Dempster, N. M. Laird and D. B. Rubin. Published in 1977 in Journal of the Royal Statistical Society, Series B, volume 39, number 1. The December 1976 presentation and later scan date are distinct from publication.
Cited passages: Section 1, printed pp. 1 and 3: naming of the two steps and earlier special cases; Section 2, printed p. 6, equation (2.17) and the general E-step/M-step definition; Section 2, printed p. 6: general maximization step; Section 3, printed pp. 6-7, Lemma 1 and Theorem 1, especially equation (3.10); Section 4.3, printed pp. 15-16, especially the paragraph following equation (4.3.3): conditional indicator probabilities and weighted counts.
Collection of sources; individual chapter authors and dates are recorded below.
The inspected chapter masthead identifies Sampling Theory, Chapter 2, Simple Random Sampling, and credits Shalabh of IIT Kanpur. Credit applies to the inspected chapter, rather than inferring authorship of every resource in a course from the host. No publication date or edition established.
Cited passages: Sampling Theory, Chapter 2, PDF pp. 10–12: sample-variance and standard-error estimation; Sampling Theory, Chapter 2, PDF pp. 2, 6–9: variance normalizations, unbiasedness, covariance derivation and finite population correction; Sampling Theory, Chapter 2, Simple Random Sampling, PDF pp. 1–4: replacement conventions and ordered versus unordered sample probabilities.
The linked section discusses events and random variables. Its terminology includes a measurable structure with the sample space; this wiki names the underlying set and its sigma-algebra separately.
Cited passages: Right Distribution Function; A General Definition.
Additional section: Conditional Probability.
Cited passages: Probability Spaces, §4 Conditional Probability, Definitions and Interpretations, The Basic Definition; Basic Theory, The Multiplication Rule; Conditioning and Bayes’ Theorem, countable partition and weighted-average interpretation. Whole-textbook authorship is credited to Kyle Siegrist; no separate section byline or publication or revision date is established. The University of Alabama in Huntsville is an affiliation and project supporter, distinct from authorship; Random Services hosts the text.
Section of Random: Probability, Mathematical Statistics, Stochastic Processes by Kyle Siegrist. Whole-textbook author: Kyle Siegrist; no separate chapter byline is established. Random Services hosts the online text. No publication or revision date is established.
Cited passages: The General Pareto Distribution, Distribution Functions and Moments; Related Distributions, right-tail conditioning and exponential transformation. The section’s parameters must be matched to the shape and minimum conventions used in each application.
An authored section of the online textbook Random. No publication or update date is established.
Cited passages: Uniform Distributions on a Finite Set: definition and mass formula.
Section of Random: Probability, Mathematical Statistics, Stochastic Processes by Kyle Siegrist, authored by Kyle Siegrist. Random Services hosts the text. No separately credited section author or publication or revision date is established.
Cited passages: Basic Theory, Definitions; Distribution Functions and the Memoryless Property; Moments.
Section of Random: Probability, Mathematical Statistics, Stochastic Processes by Kyle Siegrist by Kyle Siegrist. No separate section byline or publication date is established.
University of Washington course identified by the inspected lecture heading as Autumn 2026. The course term is distinct from a lecture publication date; the URL directory 25A does not establish the term.
By Yen-Chi Chen, explicitly named on the lecture page. Authored notes in UW STAT 535: Statistical Machine Learning, Autumn 2026, hosted on the University of Washington faculty website. No separate lecture publication or revision date is established.
Cited passages: The Bootstrap, resampling procedure; High level idea of how bootstrap works, conditional empirical sampling law; Bootstrap and Statistical Functionals, conditional variance and consistency; Failure of the bootstrap, uniform-endpoint counterexample.

Bootstrap Methods: Another Look at the Jackknife by Bradley Efron, 1979 journal article (January 1979 journal publication)

0 0
By Bradley Efron, credited as B. Efron on the inspected bibliographic cover. Published in The Annals of Statistics 7(1), 1–26, January 1979. The University of Helsinki hosts the scanned copy. The access date and hosting path are distinct from publication.
Inspected locator: bibliographic cover, author, title, journal volume and issue, January 1979 and page range. Only the cover metadata was inspected; neither the article body nor abstract was inspected.
By Bradley Efron, credited as B. Efron in the Stanford Department of Statistics catalogue. Technical report BIO 32, dated July 1977. This report record is distinct from the 1979 journal article. Stanford University issues and hosts the catalogue record.
Inspected locator: Report Number BIO 32; Author(s) B. Efron; Report Date Jul 1977. Only catalogue metadata was inspected; the linked technical report body was inaccessible.
By Purnamrita Sarkar, explicitly named on the title slide. The University of Texas at Austin, Department of Statistics and Data Science, is the listed affiliation. The author’s GitHub Pages site hosts the slides. No publication, revision or course year is established.
Cited passages: PDF pp. 1–9, title and byline; independent inputs; conditional-variance bound and independent-copy form; equality for sums.
By Bradley Efron and Charles M. Stein, printed as B. Efron and C. Stein. Published in The Annals of Statistics 9(3), 586–596, 1981. The Institute of Mathematical Statistics is the publisher; Project Euclid hosts the article record.
Bibliographic verification: Publications. The journal publication is distinct from the October 1978 Stanford technical report. Full text was unavailable during inspection; only the title and publication metadata are used.
Institutional researcher profile hosted by Stanford Profiles at Stanford University. No personal profile author or publication date is established. The 1981 date in the cited publication entry belongs to the journal article.
Cited passage: Publications, The Jackknife Estimate of Variance, Efron B., Stein C., 1981; 9(3):586–596.
By Robert E. Kass and Adrian E. Raftery. Published in Journal of the American Statistical Association 90(430), 773–795, June 1995. The University of Washington hosts this scan; its 2007 scan timestamp is distinct from the original publication.
Cited passages: §3.1, p. 776, equations (1)–(2); §5.2, p. 782; §5.3, p. 783.
By Larry Wasserman. Springer Texts in Statistics; Springer Science+Business Media. Copyright 2006; preface dated July 2005. ISBN-13: 978-0387-25145-5. Carnegie Mellon University hosts this copy.
Cited passages: §2.1, printed pp. 13–15, Definition 2.1, Theorems 2.4 and 2.6; §2.4, printed p. 21, equation (2.37).
Official online course issued by Pennsylvania State University’s Department of Statistics. No individual whole-course author or publication or revision date is established; course issuance and hosting do not identify a personal author.
Lesson in STAT 414: Introduction to Probability Theory at Pennsylvania State University. No individual author byline or separate lesson date is established. The institutional search-indexed text was inspected; the direct page fetch failed.
Cited passages: §11.1, Definition 11.1; §11.2, mean and variance theorems.
By William Sealy Gosset, published under the pseudonym Student. Biometrika 6(1), 1–25, March 1908. Wikisource hosts the inspected transcription of the original paper; its editing dates are not journal publication dates.
Inspected locators: original title and Student byline; Introduction; Sections II, III and VI. Historical notation differs from the modern convention.
By John Joseph O'Connor and Edmund Frederick Robertson, credited as J J O’Connor and E F Robertson, in the University of St Andrews MacTutor History of Mathematics archive. Last Update: October 2003; this is an online revision date. William Sealy Gosset is the subject, not the author.
Inspected locators: Quick Info; opening employment paragraph; discussion of the Student pseudonym; Written by and Last Update footer.
By Philip J. Boland, contributor to the Dictionary of Irish Biography, a Royal Irish Academy project. William Sealy Gosset is the biographical subject. Originally published October 2009; last revised October 2009.
Inspected locators: opening profession and employment paragraphs; pseudonym discussion; final biographical paragraph; Publishing information.
Online manual of the SciPy project, identified as version 1.18.0 by the inspected page title. No publication date is inferred from its copyright footer.
Section of SciPy 1.18.0 documentation. The SciPy community is credited in the copyright footer; no individual section byline or publication or revision date is established. The unversioned URL served the inspected 1.18.0 manual.
Inspected locators: maximum-likelihood location estimator; even-sample median interval; scale estimator.
By Mark Newman, credited as M. E. J. Newman. Published in Contemporary Physics 46, 323–351 (2005). The inspected arXiv version 3 was revised 29 May 2006; version 1 was submitted 1 December 2004. These preprint dates are distinct from the journal publication year.
Cited passages: §II, pp. 4–5, equations (3)–(5), density and survival exponents and fitting caveat; §III.D, pp. 10–11, equations (24)–(28), fraction of a total held by an upper population fraction. Its density exponent is one greater than the positive survival exponent used for the Pareto distribution.
Software reference manual issued and hosted by the National Institute of Standards and Technology. No personal whole-manual authorship or separate manual publication date is established. Individual entries distinguish webpage dates from implementation dates.
Entry in NIST Dataplot Reference Manual. The function name is PARPDF. Issued and hosted by the National Institute of Standards and Technology; no individual author is established from the contact address. The page gives both creation and last update as 23 August 2006; April 1994 is the function implementation date, not a publication date.
Cited passages: Description, standard density and the tail-length and lower-bound parameters; footer, creation and update dates. The optional software location and scale arguments are separate from these two parameters.
Function RAYPDF in NIST Dataplot Reference Manual, issued by the National Institute of Standards and Technology; no individual byline is established. The page was created and last updated on 7 July 2004; June 2004 is the implementation date.
Cited passages: Description, including the location and scale convention; footer dates.
By Paul Lévy. Compositio Mathematica 7, 283–339; Numdam catalogs the volume as 1940. Received 29 March 1939 (p. 339).
Cited passage: §5, pp. 301–302, especially the circle-projection paragraph on p. 302.
By Georges Matheron. Economic Geology 58(8), 1246–1266; published 1 December 1963. DOI 10.2113/gsecongeo.58.8.1246.
Cited passages: p. 1246, abstract and introduction, on mining estimation. Primary text was inspected through a scan mirror; the mirror is not the author or publisher.
Locator: inversion identity on pp. 481–482. Publisher record: academic.oup.com/biomet/article-abstract/38/3-4/481/258591
By Edwin B. Wilson and Margaret M. Hilferty. Proceedings of the National Academy of Sciences 17(12), 684–688 (1931). DOI: doi.org/10.1073/pnas.17.12.684
Locator: pp. 684–688, cube-root approximation to the chi-square distribution.
Author preprint: arxiv.org/abs/1804.07203 (the inspected PDF is version 6, dated March 2022). Locator: §3.1, definition of the univariate statistic and conditions for its asymptotic normality.
By Andrew Gelman, John Carlin, Hal S. Stern, David Dunson, Aki Vehtari and Donald Rubin, as credited on the author-hosted book homepage. Third edition.
The homepage supplies the author list and an authorized PDF for noncommercial use. Cited here for the coauthorship of Hal S. Stern and the textbook’s Bayesian subject.
By Ali Rahimi and Benjamin Recht. Advances in Neural Information Processing Systems 20, 2007.
Section 3, random Fourier features, gives the spectral sampling construction and random-offset cosine feature representation.
Cited passage: Section9, Theorem9.4, printed pages32–33: deterministic number of wired-forest components and its random-walk characterization. Section4 also gives the weighted transfer-current formula.
Articles were limited to the first 100 out of 197 total.

Ancestors (3)

  1. Mathematics bibliography
  2. Mathematics
  3. Home

View article source

Discussion (0) New discussion

There are no discussions about this article yet.

Articles by others on the same topic (0)

There are currently no matching articles.
See all articles in the same topic Create my own version