Remarks on Some Nonparametric Estimates of a Density Function
1956/09/01 by Murray Rosenblatt · 4,557 citations
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Applied mathematics #Bayesian Methods and Mixture Models #Class (philosophy) #Computer science #Density estimation #Econometrics #Estimator #Function (biology) #Mathematics #Multivariate kernel density estimation #Multivariate statistics #Nonparametric statistics #Probability density function #Statistical Methods and Inference #Statistics #Univariate
paper · pdf · doi:10.1214/aoms/1177728190
published in The Annals of Mathematical Statistics 27(3), 832-837 (Institute of Mathematical Statistics)
openalex publication_date 1956/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Abstract
This note discusses some aspects of the estimation of the density function of a univariate probability distribution. All estimates of the density function satisfying relatively mild conditions are shown to be biased. The asymptotic mean square error of a particular class of estimates is evaluated.
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