Deconvolution density estimation on the space of positive definite symmetric matrices

Peter T. Kim; Donald St P. Richards

doi:10.1142/9789814340564_0010

Deconvolution density estimation on the space of positive definite symmetric matrices

Peter T. Kim, Donald St P. Richards

Statistics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

12 Scopus citations

Abstract

Motivated by applications in microwave engineering and diffusion tensor imaging, we study the problem of deconvolution density estimation on the space of positive definite symmetric matrices. We develop a nonparametric estimator for the density function of a random sample of positive definite matrices. Our estimator is based on the Helgason-Fourier transform and its inversion, the natural tools for analysis of compositions of random positive definite matrices. Under several smoothness conditions on the density of the intrinsic error in the random sample, we derive upper bounds on the rates of convergence of our nonparametric estimator to the true density.

Original language	English (US)
Title of host publication	Nonparametric Statistics and Mixture Models
Subtitle of host publication	A Festschrift in Honor of Thomas P Hettmansperger
Publisher	World Scientific Publishing Co.
Pages	147-168
Number of pages	22
ISBN (Electronic)	9789814340564
ISBN (Print)	9814340553, 9789814340557
DOIs	https://doi.org/10.1142/9789814340564_0010
State	Published - Jan 1 2011

All Science Journal Classification (ASJC) codes

Mathematics(all)

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Deconvolution density estimation on the space of positive definite symmetric matrices

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