Minimax estimation for mixtures of wishart distributions

L. R. Haff, P. T. Kim, J. Y. Koo, D. St. P. Richards

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The space of positive definite symmetric matrices has been studied extensively as a means of understanding dependence in multivariate data along with the accompanying problems in statistical inference. Many books and papers have been written on this subject, and more recently there has been considerable interest in high-dimensional random matrices with particular emphasis on the distribution of certain eigenvalues. With the availability of modern data acquisition capabilities, smoothing or nonparametric techniques are required that go beyond those applicable only to data arising in Euclidean spaces. Accordingly, we present a Fourier method of minimax Wishart mixture density estimation on the space of positive definite symmetric matrices.

Original languageEnglish (US)
Pages (from-to)3417-3440
Number of pages24
JournalAnnals of Statistics
Volume39
Issue number6
DOIs
StatePublished - Dec 2011

Fingerprint

Minimax Estimation
Wishart Distribution
Symmetric Positive Definite Matrix
Fourier Method
Multivariate Data
Density Estimation
Statistical Inference
Random Matrices
Data Acquisition
Minimax
Euclidean space
Smoothing
High-dimensional
Availability
Eigenvalue

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Haff, L. R. ; Kim, P. T. ; Koo, J. Y. ; St. P. Richards, D. / Minimax estimation for mixtures of wishart distributions. In: Annals of Statistics. 2011 ; Vol. 39, No. 6. pp. 3417-3440.
@article{fb8fddca650d4afda6879244d8997458,
title = "Minimax estimation for mixtures of wishart distributions",
abstract = "The space of positive definite symmetric matrices has been studied extensively as a means of understanding dependence in multivariate data along with the accompanying problems in statistical inference. Many books and papers have been written on this subject, and more recently there has been considerable interest in high-dimensional random matrices with particular emphasis on the distribution of certain eigenvalues. With the availability of modern data acquisition capabilities, smoothing or nonparametric techniques are required that go beyond those applicable only to data arising in Euclidean spaces. Accordingly, we present a Fourier method of minimax Wishart mixture density estimation on the space of positive definite symmetric matrices.",
author = "Haff, {L. R.} and Kim, {P. T.} and Koo, {J. Y.} and {St. P. Richards}, D.",
year = "2011",
month = "12",
doi = "10.1214/11-AOS951",
language = "English (US)",
volume = "39",
pages = "3417--3440",
journal = "Annals of Statistics",
issn = "0090-5364",
publisher = "Institute of Mathematical Statistics",
number = "6",

}

Minimax estimation for mixtures of wishart distributions. / Haff, L. R.; Kim, P. T.; Koo, J. Y.; St. P. Richards, D.

In: Annals of Statistics, Vol. 39, No. 6, 12.2011, p. 3417-3440.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Minimax estimation for mixtures of wishart distributions

AU - Haff, L. R.

AU - Kim, P. T.

AU - Koo, J. Y.

AU - St. P. Richards, D.

PY - 2011/12

Y1 - 2011/12

N2 - The space of positive definite symmetric matrices has been studied extensively as a means of understanding dependence in multivariate data along with the accompanying problems in statistical inference. Many books and papers have been written on this subject, and more recently there has been considerable interest in high-dimensional random matrices with particular emphasis on the distribution of certain eigenvalues. With the availability of modern data acquisition capabilities, smoothing or nonparametric techniques are required that go beyond those applicable only to data arising in Euclidean spaces. Accordingly, we present a Fourier method of minimax Wishart mixture density estimation on the space of positive definite symmetric matrices.

AB - The space of positive definite symmetric matrices has been studied extensively as a means of understanding dependence in multivariate data along with the accompanying problems in statistical inference. Many books and papers have been written on this subject, and more recently there has been considerable interest in high-dimensional random matrices with particular emphasis on the distribution of certain eigenvalues. With the availability of modern data acquisition capabilities, smoothing or nonparametric techniques are required that go beyond those applicable only to data arising in Euclidean spaces. Accordingly, we present a Fourier method of minimax Wishart mixture density estimation on the space of positive definite symmetric matrices.

UR - http://www.scopus.com/inward/record.url?scp=84878241207&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84878241207&partnerID=8YFLogxK

U2 - 10.1214/11-AOS951

DO - 10.1214/11-AOS951

M3 - Article

AN - SCOPUS:84878241207

VL - 39

SP - 3417

EP - 3440

JO - Annals of Statistics

JF - Annals of Statistics

SN - 0090-5364

IS - 6

ER -