NDLI: Frequent problems in calculating integrals and optimizing objective functions: a case study in density deconvolution

Content Provider	Springer Nature Link
Author	Delaigle, A. Gijbels, I.
Copyright Year	2007
Abstract	Many statistical procedures involve calculation of integrals or optimization (minimization or maximization) of some objective function. In practical implementation of these, the user often has to face specific problems such as seemingly numerical instability of the integral calculation, choices of grid points, appearance of several local minima or maxima, etc. In this paper we provide insights into these problems (why and when are they happening?), and give some guidelines of how to deal with them. Such problems are not new, neither are the ways to deal with them, but it is worthwhile to devote serious considerations to them. For a transparant and clear discussion of these issues, we focus on a particular statistical problem: nonparametric estimation of a density from a sample that contains measurement errors. The discussions and guidelines remain valid though in other contexts. In the density deconvolution setting, a kernel density estimator has been studied in detail in the literature. The estimator is consistent and fully data-driven procedures have been proposed. When implemented in practice however, the estimator can turn out to be very inaccurate if no adequate numerical procedures are used. We review the steps leading to the calculation of the estimator and in selecting parameters of the method, and discuss the various problems encountered in doing so.
Starting Page	349
Ending Page	355
Page Count	7
File Format	PDF
ISSN	09603174
Journal	Statistics and Computing
Volume Number	17
Issue Number	4
e-ISSN	15731375
Language	English
Publisher	Springer US
Publisher Date	2007-08-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Bandwidth selection Dramatic cancellation Fast Fourier transform Numerical approximations Optimization Artificial Intelligence (incl. Robotics) Mathematics Numeric Computing Statistics Statistics and Computing/Statistics Programs
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Theoretical Computer Science Computational Theory and Mathematics Statistics, Probability and Uncertainty

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