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Gaussian deconvolution via differentiation
Author(s) -
Masry Elias,
Rice John A.
Publication year - 1992
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 - 10.2307/3315571
Subject(s) - pointwise , deconvolution , convolution (computer science) , gaussian , mathematics , norm (philosophy) , statistics , computer science , mathematical analysis , physics , artificial intelligence , quantum mechanics , artificial neural network , political science , law
Suppose that ϕ is a Gaussian density and that g = f * ϕ, where * denotes convolution. From observations with density g, one wishes to estimate f. We analyze an estimate which is a linear combination of estimates of derivatives of g and show that this estimate converges in an L 2 norm at a rate which is compatible with the pointwise optimal rate established by Fan (1991).