Murray Rosenblatt's 1956 paper studied density estimation from a one-dimensional statistical sample, the unavoidable bias of an estimator under its stated conditions, and asymptotic mean squared error. It is an early foundation of kernel density estimation. [ref]
https://doi.org/10.1214/aoms/1177728190. Rosenblatt, Remarks on Some Nonparametric Estimates of a Density Function, Annals of Mathematical Statistics 27(3), 832-837 (1956)
. Emanuel Parzen's 1962 paper developed statistical consistency and asymptotic normality for probability density function estimates and studied estimation of the mode. [ref]https://doi.org/10.1214/aoms/1177704472. Parzen, On Estimation of a Probability Density Function and Mode, Annals of Mathematical Statistics 33(3), 1065-1076 (1962)
.The authors' interests help explain the connection with smoothing. In a conversation recorded in 2006 and published in 2009, Rosenblatt recalled that his density estimation work grew out of estimation of the time-series spectral density and emphasized the connection with a smoothed histogram. This is his retrospective account of the motivation. [ref]
https://celebratio.org/Rosenblatt_M/article/891/. Brillinger and Davis, A conversation with Murray Rosenblatt, passage immediately before The Chicago, Indiana and Brown years
. Parzen's original paper lists Stanford University as his affiliation; its opening frames the problem as recovering both a probability density function and its mode from independent and identically distributed random variables. [ref]. Articles by others on the same topic
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