We study a new approach to simultaneous variable selection and estimation via random-effect models. Introducing random effects as the solution of a regularization problem is a flexible paradigm and accommodates likelihood interpretation for variable selection. This approach leads to a new type...

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...

We consider a noisy observed vector y=x+u∈Rn. The unobserved vector x is a solution of a non-invertible linear system Ax=v, where v is a forcing term. A unique solution of the system is obtained by considering additional constraint on the vector x. This constraint is defined by a triple...

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....

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...

We report a matrix expression for the covariance matrix of MLEs of factor loadings in factor analysis. We then derive the analytical formula for covariance matrix of the covariance estimators of MLEs of factor loadings by obtaining the matrix of partial derivatives, which maps the differential...