This paper establishes asymptotic results for the maximum likelihood and restricted (REML) estimators of parameters in nested error regression model clustered data when both number independent clusters cluster sizes (the observations each cluster) go to infinity. Under very mild conditions, are shown be asymptotically normal with an elegantly structured covariance matrix. There no restrictions ...

Lognormal linear models are widely used in applications, and many times it is of interest to predict the response variable at the original scale for a new set of covariate values. In this paper we consider the problem of efficient estimation of the conditional mean of the response variable at the original scale for lognormal linear models. Several existing estimators are reviewed, including the...

In a spatial regression context, scientists are often interested in a physical interpretation of components of the parametric covariance function. For example, spatial covariance parameter estimates in ecological settings have been interpreted to describe spatial heterogeneity or “patchiness” in a landscape that cannot be explained by measured covariates. In this article, we investigate the inf...

Autoregressive moving average (ARMA) models are useful statistical tools to examine the dynamical characteristics of ecological time-series data. Here, we illustrate the utility and challenges of applying ARMA (p,q) models, where p is the dimension of the autoregressive component of the model, and q is the dimension of the moving average component. We focus on parameter estimation and model sel...

In this paper we consider two closely related problems: estimation of eigenvalues and eigenfunctions of the covariance kernel of functional data based on (possibly) irregular measurements, and the problem of estimating the eigenvalues and eigenvectors of the covariance matrix for highdimensional Gaussian vectors. In [A geometric approach to maximum likelihood estimation of covariance kernel fro...

In this paper we consider two closely related problems : estimation of eigenvalues and eigenfunctions of the covariance kernel of functional data based on (possibly) irregular measurements, and the problem of estimating the eigenvalues and eigenvectors of the covariance matrix for high-dimensional Gaussian vectors. In Peng and Paul (2007), a restricted maximum likelihood (REML) approach has bee...

Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixedand random-effects terms. The formula and data together determine a numerical repr...

The multiple-trait derivative-free REML set of programs was written to handle partially missing data for multiple-trait analyses as well as single-trait models. Standard errors of genetic parameters were reported for univariate models and for multiple-trait analyses only when all traits were measured on animals with records. In addition to estimating (co)variance components for multiple-trait m...