The necessary and sufficient conditions for the weighted least-squares estimators (WLSEs) of parametric functions K1β1+K2β2+⋯+Kmβm under a multiple partitioned linear model ℳ={y,X1β1+⋯+Xmβm,σ2Σ} to be the sum of the WLSEs of Kiβi under the m small models...

Inference for variance components in linear mixed models of ANOVA type, including estimation and testing, has been investigated when the number of fixed effects is fixed. However, for high-dimensional data, this number is large and would be regarded as a divergent value as the sample size goes...

Maximum entropy models, motivated by applications in neuron science, are natural generalizations of the β-model to weighted graphs. Similar to the β-model, each vertex in maximum entropy models is assigned a potential parameter, and the degree sequence is the natural sufficient statistic....

Principal subspace theorems deal with the problem of finding subspaces supporting optimal approximations of multivariate distributions. The optimality criterion considered in this paper is the minimization of the mean squared distance between the given distribution and an approximating...

A factor analysis-based approach for estimating high dimensional covariance matrix is proposed and is applied to solve the mean–variance portfolio optimization problem in finance. The consistency of the proposed estimator is established by imposing a factor model structure with a relative weak...

Classification arises in a wide range of applications. A variety of statistical tools have been developed for learning classification rules from data. Understanding of their relative merits and comparisons help users to choose a proper method in practice. This paper focuses on theoretical...

Functional mixed-effects models are very useful in analyzing data. In this paper, we consider a functional mixed-effects model, where the observations are the real functions, and derive the maximum likelihood estimators of the functional parameters and variance components. The properties of the...

Statistical methods for functional data are of interest for many applications. In this paper, we prove a central limit theorem for random variables taking their values in a Hilbert space. The random variables are assumed to be weakly dependent in the sense of near epoch dependence, where the...

Sliced inverse regression (SIR) is a widely used non-parametric method for supervised dimension reduction. Conventional SIR mainly tackles simple data structure but is inappropriate for data with array (tensor)-valued predictors. Such data are commonly encountered in modern biomedical imaging...

For a standard tool in econometrics, matrix calculus, an approach is illustrated in this note that is unusual in that context, a coordinate-free approach. It can help to eliminate the persistent use of non-standard conventions. The Kronecker product and its use can be better understood. The...