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...

The authors explore likelihood-based methods for making inferences about the components of variance in a general normal mixed linear model. In particular, they use local asymptotic approximations to construct confidence intervals for the components of variance when the components are close to the boundary of the parameter space. In the process, they explore the question of how to profile the re...

The widespread use of the set of multiple-trait derivative-free REML programs for prediction of breeding values and estimation of variance components has led to significant improvement in traits of economic importance. The initial version of this software package, however, was generally limited to pedigree-based relationships. With continued advances in genomic research and the increased availa...

In order to ascertain changes in bitterness as beer aged naturally, time±intensity (TI) measurements were made by a professional sensory panel using a squeezer transducer system. TI parameters were ®tted by variance components models using Restricted Maximum Likelihood (REML). It was shown that bitterness decreased with age, although this age-induced di€erence was smaller than the original di€e...

Six packages for solving mixed model equations and estimating variance components by REML are compared. Each has a unique strength. Meticulously finished DFREML is the only one that implements hypothesis testing for variance component estimates. MTDFREML is a comprehensive, relatively easy to install and simple to use package for analyses of experimental data. PEST, the only semi-commercial pro...

INTRODUCTION Random regression (RR) models for longitudinal data often require a considerable number of parameters to describe the associated covariance functions. Estimation of these parameters has proven cumbersome and subject to sampling problems. Moreover, computational restraints have limited analyses of data sets sufficiently large to supply accurate estimates. This holds especially for c...