Deconvolution density estimation on the space of positive definite symmetric matrices

Peter T. Kim, Donald Richards

Research output: Chapter in Book/Report/Conference proceedingChapter

7 Citations (Scopus)

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 languageEnglish (US)
Title of host publicationNonparametric Statistics and Mixture Models
Subtitle of host publicationA Festschrift in Honor of Thomas P Hettmansperger
PublisherWorld Scientific Publishing Co.
Pages147-168
Number of pages22
ISBN (Electronic)9789814340564
ISBN (Print)9814340553, 9789814340557
DOIs
StatePublished - Jan 1 2011

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Symmetric Positive Definite Matrix
Deconvolution
Density Estimation
Positive definite matrix
Nonparametric Estimator
Density Function
Microwave
Smoothness
Fourier transform
Inversion
Rate of Convergence
Tensor
Imaging
Upper bound
Engineering
Estimator

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Kim, P. T., & Richards, D. (2011). Deconvolution density estimation on the space of positive definite symmetric matrices. In Nonparametric Statistics and Mixture Models: A Festschrift in Honor of Thomas P Hettmansperger (pp. 147-168). World Scientific Publishing Co.. https://doi.org/10.1142/9789814340564_0010
Kim, Peter T. ; Richards, Donald. / Deconvolution density estimation on the space of positive definite symmetric matrices. Nonparametric Statistics and Mixture Models: A Festschrift in Honor of Thomas P Hettmansperger. World Scientific Publishing Co., 2011. pp. 147-168
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Kim, PT & Richards, D 2011, Deconvolution density estimation on the space of positive definite symmetric matrices. in Nonparametric Statistics and Mixture Models: A Festschrift in Honor of Thomas P Hettmansperger. World Scientific Publishing Co., pp. 147-168. https://doi.org/10.1142/9789814340564_0010

Deconvolution density estimation on the space of positive definite symmetric matrices. / Kim, Peter T.; Richards, Donald.

Nonparametric Statistics and Mixture Models: A Festschrift in Honor of Thomas P Hettmansperger. World Scientific Publishing Co., 2011. p. 147-168.

Research output: Chapter in Book/Report/Conference proceedingChapter

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Kim PT, Richards D. Deconvolution density estimation on the space of positive definite symmetric matrices. In Nonparametric Statistics and Mixture Models: A Festschrift in Honor of Thomas P Hettmansperger. World Scientific Publishing Co. 2011. p. 147-168 https://doi.org/10.1142/9789814340564_0010