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 | |
| State | Published - Jan 1 2011 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
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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 proceeding › Chapter
TY - CHAP
T1 - Deconvolution density estimation on the space of positive definite symmetric matrices
AU - Kim, Peter T.
AU - Richards, Donald
PY - 2011/1/1
Y1 - 2011/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84973121263&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84973121263&partnerID=8YFLogxK
U2 - 10.1142/9789814340564_0010
DO - 10.1142/9789814340564_0010
M3 - Chapter
SN - 9814340553
SN - 9789814340557
SP - 147
EP - 168
BT - Nonparametric Statistics and Mixture Models
PB - World Scientific Publishing Co.
ER -