= History of kernel density estimation
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>. 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)]{ref}. Emanuel Parzen's 1962 paper developed <statistical consistency> and <asymptotic normality> for <probability density function> estimates and studied estimation of the <mode>. 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)]{ref}.
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. https://celebratio.org/Rosenblatt_M/article/891/[Brillinger and Davis, A conversation with Murray Rosenblatt, passage immediately before The Chicago, Indiana and Brown years]{ref}. 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>. https://bayes.wustl.edu/Manual/Parzen_1962.pdf[Parzen's original paper, p. 1065]{ref}.
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