In this paper, we study the problem of estimating the covariance matrix [Sigma] and the precision matrix [Omega] (the inverse of the covariance matrix) in a star-shape model with missing data. By considering a type of Cholesky decomposition of the precision matrix [Omega]=[Psi]'[Psi], where...

Identified vector autoregressive (VAR) models have become widely used on time series data in recent years, but finite sample inference for such models remains a challenge. In this study, we propose a conjugate prior for Bayesian analysis of normalized VAR models. Under the prior, the marginal...

The conditional autoregressive (CAR) and simultaneous autoregressive (SAR) models both have been used extensively for the analysis of spatial structure underlying lattice data in many areas, such as epidemiology, demographics, economics, and geography. Default Bayesian analyses have been...

In this paper we propose a new test procedure for sphericity of the covariance matrix when the dimensionality, p, exceeds that of the sample size, N=n+1. Under the assumptions that (A) as p--[infinity] for i=1,...,16 and (B) p/n--c<[infinity] known as the concentration, a new statistic is developed utilizing the ratio of the fourth and second arithmetic means of the eigenvalues of the sample covariance matrix. The newly defined test has many desirable general asymptotic properties, such as normality and consistency when (n,p)-->[infinity]. Our simulation results show that the new test is...</[infinity]>