Many modern statistical problems can be cast in the framework of multivariate regression, where the main task is to make statistical inference for a possibly sparse and low-rank coefficient matrix. The low-rank structure in the coefficient matrix is of intrinsic multivariate nature, which, when combined with sparsity, can further lift dimension reduction, conduct variable selection, and facilit...

Outlier detection statistics based on two models, the case-deletion model and the mean-shift model, are developed in the context of a multivariate linear regression model. These are generalizations of the univariate Cook’s distance and other diagnostic statistics. Approximate distributions of the proposed statistics are also obtained to get suitable cutoff points for significance tests. In addi...

Variance function estimation in multivariate nonparametric regression is considered and the minimax rate of convergence is established. Our work uses the approach that generalizes the one used in Munk et al (2005) for the constant variance case. As is the case when the number of dimensions d = 1, and very much contrary to the common practice, it is often not desirable to base the estimator of t...

We discuss the application of the GHK simulation method for maximum likelihood estimation of the multivariate probit regression model and describe and illustrate a Stata program mvprobit for this purpose.

Traditionally multivariate calibration models have been developed using regression based techniques including principal component regression and partial least squares and their non-linear counterparts. This paper proposes the application of Gaussian process regression as an alternative method for the development of a calibration model. By formulating the regression problem in a probabilistic fr...

In insurance and related industries including healthcare, it is common to have several outcome measures that the analyst wishes to understand using explanatory variables. For example, in automobile insurance, an accident may result in payments for damage to one’s own vehicle, damage to another party’s vehicle, or personal injury. It is also common to be interested in the frequency of accidents ...

We consider the problem of regression on multivariate count data and present a Gibbs sampler for a latent feature regression model suitable for both underand overdispersed response variables. The model learns countvalued latent features conditional on arbitrary covariates, modeling them as negative binomial variables, and maps them into the dependent count-valued observations using a Dirichlet-...

A similarity matrix is a covariance matrix generated by additive nested common factors having independent components. The set of such matrices is a structured subset of covariance matrices, closed under permutation and restriction, which makes it potentially useful as a sub-model for the joint dependence of several responses. It is also equal to the set of rooted trees. Some issues connected wi...