In the spiked population model introduced by Johnstone (2001) [11], the population covariance matrix has all its eigenvalues equal to unit except for a few fixed eigenvalues (spikes). The question is to quantify the effect of the perturbation caused by the spike eigenvalues. Baik and Silverstein...

The product moments of existing and new noncentral bimatrix variate beta distributions with bounded domain are derived. From these, exact expressions for the distributions of statistics are obtained by using the Mellin transform. These distributions add value to multivariate statistical analysis...

Validity of Wagle’s multivariate extension of the Durbin randomization device is directly proved and some vague points of the original paper are clarified. The device is then used in a non-standard way to obtain asymptotic distributions of some functions of the multivariate Gaussian sample...

In Bayesian disease mapping, one needs to specify a neighborhood structure to make inference about the underlying geographical relative risks. We propose a model in which the neighborhood structure is part of the parameter space. We retain the Markov property of the typical Bayesian spatial...

We consider one-step estimation of parameters that represent the strength of spatial dependence in a geostatistical or lattice spatial model. While the maximum likelihood estimators (MLE) of spatial dependence parameters are known to have various desirable properties, they do not have...

In this paper we propose James–Stein type estimators for variances raised to a fixed power by shrinking individual variance estimators towards the arithmetic mean. We derive and estimate the optimal choices of shrinkage parameters under both the squared and the Stein loss functions. Asymptotic...

Given a multinomial decomposable graphical model, we identify several alternative parametrizations; in particular we consider conditional probabilities of clique-residuals given separators, as well as generalized log-odds-ratios. For each such parametrization, we construct the corresponding...

The empirical best linear unbiased predictor (EBLUP) in the linear mixed model (LMM) is useful for the small area estimation, and the estimation of the mean squared error (MSE) of EBLUP is important as a measure of uncertainty of EBLUP. To obtain a second-order unbiased estimator of the MSE, the...

As a useful tool in functional data analysis, the functional linear regression model has become increasingly common and been studied extensively in recent years. In this paper, we consider a sparse functional linear regression model which is generated by a finite number of basis functions in an...

We derive the asymptotical distributions of two-sample U-statistics and two-sample empirical U-quantiles in the case of weakly dependent data. Our results apply to observations that can be represented as functionals of absolutely regular processes, including e.g. many classical time series...