A COVARIANCE REGRESSION MODEL

作者：Hoff Peter D^*; Niu Xiaoyue

来源：Statistica Sinica, 2012, 22(2): 729-753.

DOI：10.5705/ss.2010.051

• Heteroscedasticity
• positive definite cone
• random effects

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.

• 出版日期2012-4