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On the Optimal Rates of Convergence for Nonparametric Deconvolution Problems
The Annals of Statistics
Vol. 19, No. 3 (Sep., 1991), pp. 1257-1272
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2241949
Page Count: 16
You can always find the topics here!Topics: Density estimation, Estimators, Random variables, Statism, Density, Mathematical constants, Point estimators, Fourier transformations, Eigenfunctions, Kernel functions
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Deconvolution problems arise in a variety of situations in statistics. An interesting problem is to estimate the density f of a random variable X based on n i.i.d. observations from Y = X + ε, where ε is a measurement error with a known distribution. In this paper, the effect of errors in variables of nonparametric deconvolution is examined. Insights are gained by showing that the difficulty of deconvolution depends on the smoothness of error distributions: the smoother, the harder. In fact, there are two types of optimal rates of convergence according to whether the error distribution is ordinary smooth or supersmooth. It is shown that optimal rates of convergence can be achieved by deconvolution kernel density estimators.
The Annals of Statistics © 1991 Institute of Mathematical Statistics