A covariance regression model

Peter D. Hoff, Xiaoyue Niu

Research output: Contribution to journalArticle

30 Citations (Scopus)

Abstract

Classical regression analysis relates the expectation of a response variable to a linear combination of explanatory variables. In this article, we propose a covariance regression model that parameterizes the covariance matrix of a multivariate response vector as a parsimonious quadratic function of explanatory variables. The approach is analogous to the mean regression model, and is similar to a factor analysis model in which the factor loadings depend on the explanatory variables. Using a random-effects representation, parameter estimation for the model is straightforward using either an EM-algorithm or an MCMC approximation via Gibbs sampling. The proposed methodology provides a simple but flexible representation of heteroscedasticity across the levels of an explanatory variable, improves estimation of the mean function and gives better calibrated prediction regions when compared to a homoscedastic model.

Original languageEnglish (US)
Pages (from-to)729-753
Number of pages25
JournalStatistica Sinica
Volume22
Issue number2
DOIs
StatePublished - Apr 1 2012

Fingerprint

Regression Model
Multivariate Response
Heteroscedasticity
Parameterise
Gibbs Sampling
EM Algorithm
Factor Analysis
Markov Chain Monte Carlo
Quadratic Function
Random Effects
Regression Analysis
Covariance matrix
Parameter Estimation
Linear Combination
Regression model
Model
Methodology
Prediction
Approximation

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Hoff, Peter D. ; Niu, Xiaoyue. / A covariance regression model. In: Statistica Sinica. 2012 ; Vol. 22, No. 2. pp. 729-753.
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A covariance regression model. / Hoff, Peter D.; Niu, Xiaoyue.

In: Statistica Sinica, Vol. 22, No. 2, 01.04.2012, p. 729-753.

Research output: Contribution to journalArticle

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