By Victor Chernozhukov and others.

Author text: arxiv.org/pdf/1608.00060v6

Version-specific title and byline verified on PDF page 1; arXiv:1608.00060v6 dated 12 December 2017. Cited passages: Section 2.1, Neyman orthogonality; Section 3, Definitions 3.1–3.2, cross-fitting/DML constructions and nuisance-rate conditions; Section 5.1, equation (5.3) and Theorem 5.1, orthogonal average-treatment-effect score and asymptotic inference. The later arXiv v7 changes Structural to Causal in the title; this card refers specifically to v6.

Primary text: users.stat.umn.edu/~helwig/notes/generalized-linear-models.html

Cited passages: Section 1, Deviance and Estimating phi: unscaled deviance, dispersion normalization and residual-degree moment estimates. Instructor-authored University of Minnesota notes; their opening attribution identifies the summarized portions of Simon N. Wood, Generalized Additive Models, second edition, chapter 3.

Primary text: www.stat.cmu.edu/~cshalizi/TALR/TALR.pdf

Cited passages: Chapter 21, section 21.3, printed pp. 363–365: Gauss–Markov optimality among response-linear unbiased estimators under stated covariance assumptions. The manuscript distinguishes optimal linear prediction from additional Gaussian sampling assumptions.

Primary text: arxiv.org/pdf/1009.5689

Cited passages: Section 1, equations (8)–(11), printed pp. 2–4: square-root loss and pivotal score. The inspected version is arXiv:1009.5689v5 (18 December 2011), accompanying the Biometrika paper, DOI 10.1093/biomet/asr043.

Primary text: arxiv.org/pdf/1409.8557

Cited passages: Sections 1.3–1.4, printed pp. 6–12: normalized Lasso and square-root Lasso objectives and prediction inequalities. Section 2.4, Theorems 2.4.1–2.4.2, printed pp. 18–19: linear-noise expansion, coefficient-error remainder and Gaussian normalization of de-sparsified Lasso.

Primary text: arxiv.org/pdf/math/0106036

Cited passages: Section 6, Theorem 6.1, Lemma 6.6 and Theorem 6.4, printed pp. 23 and 29–31: boundary avoidance below parameter eight versus visiting swallowed points at and above eight. Section 3 gives the reverse-flow derivative method. The inspected version is arXiv:math/0106036v4 (20 January 2004); section 9 records the later proof of trace existence at parameter eight.

Primary text: www.stat.berkeley.edu/~bartlett/courses/153-fall2010/lectures/20.pdf

Cited passages: Slides 2–9: periodogram definition, interior-frequency Gaussian Fourier coefficients and nonvanishing exponential-limit variance. The course homepage identifies Peter Bartlett as instructor. These slides use cycles-per-observation normalization; the wiki explicitly converts to angular frequency.

Primary text: www.stat.colostate.edu/~piotr/horvathKokoszkaReeder2013.pdf

Cited passages: Sections 2–3, Theorems 1, 3 and 5 and equations (3.6), (3.13)–(3.15), printed pp. 105–110: Hilbert-space Gaussian mean limits, pooled two-sample covariance and weighted chi-squared norm laws. Independent curves are the special case with no serial covariance. Journal of the Royal Statistical Society Series B 75(1), pp. 103–122, DOI 10.1111/j.1467-9868.2012.01032.x.

By Rick Durrett.

Theorems 1–2 construct the maximal stationary law and state contact-process self-duality; the following single-site identity equates equilibrium occupation with finite-seed survival. The page uses the square lattice, a death-rate parameter and birth rates normalized by neighbour count.

By Steven L. Heston. The Review of Financial Studies 6(2), pages 327–343.

Publisher: doi.org/10.1093/rfs/6.2.327

Original paper: finance.martinsewell.com/stylized-facts/volatility/Heston1993.pdf

Introduces the Heston model and its characteristic-function approach to option pricing, including correlation between return and variance innovations.

By Fischer Black, Myron Scholes. Journal of Political Economy 81(3), pages 637–654, May–June 1973.

Publisher: www.journals.uchicago.edu/doi/10.1086/260062

Original paper: finance.martinsewell.com/option-pricing/BlackScholes1973.pdf

Develops the option-replication argument and the Black-Scholes model pricing equation.

Author-hosted lecture notes: www.gatsby.ucl.ac.uk/~gretton/coursefiles/RKHS_Notes1.pdf

The title page gives both authors and 11 March2012. Consulted passage: section6.2, Theorem48, printed p21: continuous kernel on a compact metric space, finite Borel measure of full support, positive-eigenvalue expansion, uniform convergence and pointwise absolute convergence. The surrounding text fixes a positive-definite kernel and chooses continuous representatives of eigenfunctions.

By Peter Hall.

Publisher: link.springer.com/book/10.1007/978-1-4612-4384-7

Chapter scan: people.eecs.berkeley.edu/~jordan/sail/readings/edgeworth.pdf

Chapter 2, Principles of Edgeworth Expansion, pages 39–81: cumulant/characteristic-function expansions, smoothness conditions and lattice corrections. The publisher identifies the original 1992 copyright; its 2013 electronic publication is not a new edition. The wiki states a stronger smooth-density sufficient setting and derives its first correction explicitly.

By Richard Pymar, Nicolás Rivera.

arXiv:2112.01478v2, 1 October 2024. Sections 1.1–1.2 define uniform single-vertex updates, fair rerandomization and the copying kernel. The weighted-Hamming contraction calculation in the wiki is derived explicitly for a finite undirected graph; its time unit is one vertex update, rather than one update per vertex.

By Sharad Goel, Ravi Montenegro, Prasad Tetali.

Author-hosted primary paper; arXiv:math/0505690 (2005). Section 1.2, Definitions 1.4–1.5 define the variance-normalized spectral profile. Section 2.2, Definition 2.2 and Lemma 2.4 compare it with the conductance profile. Section 1.1 defines stationary reversibility.

Consulted passages: Definition 3.1, Remark 3.2 and Claim 3.2, printed p.28 (measurable-fibre Steiner symmetrization and volume preservation).

The official course page credits the notes to students with editing by Galyna Livshyts.

Original paper: derivativesacademy.com/storage/uploads/files/modules/resources/1702215622_breeden_and_litzenberger_1978_prices_of_state_contingent_claims_implicit_in_option_prices.pdf

Author-deposited record: papers.ssrn.com/sol3/papers.cfm?abstract_id=2642349

Journal of Business51(4), October1978, pp621–651. Consulted sectionII, printed pp625–627, call-spread replication and second-strike-derivative state prices, especially equation(2). The later electronic posting is not the original publication date.

Author-hosted lecture slides: people.math.ethz.ch/~jteichma/slides_ftap.pdf

Consulted passages: slides165–170, finite-discrete-time martingale-measure theorem and one-period convex-hull argument; slides198–200, replication and uniqueness. Title page specifies Autumn term2020. The source treats broader models; the elementary wiki example restricts to a finite state space.

By Ismaël Castillo, Richard Nickl.

Annals of Statistics 41(4), 1999–2028. DOI: doi.org/10.1214/13-AOS1133 . Section 2.3.1: inference on linear functionals and required regularity; conjugate product-prior formulas and explicit bias condition in the wiki are independent calculations.

By Scott Sheffield.

arXiv math/0312099v3, 23 November 2006. Section 2: Hilbert/Dirichlet-space and basis constructions; Section 2.8: circle averages. The wiki explicitly chooses its own 1/(2pi) energy normalization and associated logarithmic Green kernel.