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A consistent nonparametric density estimator for the deconvolution problem
Author(s) -
Liu Ming Chung,
Taylor Robert L.
Publication year - 1989
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315482
Subject(s) - estimator , deconvolution , mathematics , kernel density estimation , nonparametric statistics , probability density function , upper and lower bounds , statistics , kernel (algebra) , consistent estimator , minimax estimator , mean squared error , combinatorics , mathematical analysis , minimum variance unbiased estimator
The problem of nonparametric estimation of a probability density function when the sample observations are contaminated with random noise is studied. A particular estimator f̌ n (x) is proposed which uses kernel‐density and deconvolution techniques. The estimator f̌ n (x) is shown to be uniformly consistent, and its appearance and properties are affected by constants M n and h n which the user may choose. The optimal choices of M n and h n depend on the sample size n , the noise distribution, and the true distribution which is being estimated. Particular selections for M n and h n which minimize upper‐bound functions of the mean squared error for f̌ n (x) are recommended.