We propose a method of analyzing collections of related curves in which the individual curves are modeled as spline functions with random coefficients. The method is applicable when the individual curves are sampled at variable and irregularly spaced points. This produces a low-rank, low-frequency approximation to the covariance structure, which can be estimated naturally by the EM algorithm. S...

The problem of accurately estimating the mean-squared error of small area estimators within a Fay–Herriot normal error model is studied theoretically in the common setting where the model is fitted to a logarithmically transformed response variable. For bias-corrected empirical best linear unbiased predictor small area point estimators, mean-squared error formulae and estimators are provided, w...

We consider the problem of constructing metamodels for computationally expensive simulation codes; that is, we construct interpolation/prediction of functions values (responses) from a finite collection of evaluations (observations). We use Gaussian process modeling and Kriging, and combine a Bayesian approach, based on a finite set of covariance functions, with the use of localized models, ind...

Milk fatty acids (FA) have been suggested as biomarkers for early-lactation metabolic diseases and female fertility status. The aim of the present study was to infer associations between FA, disorder ketosis (KET), interval from calving first insemination (ICF) genetically genomically. In this regard, we focused on a single-step genomic BLUP approach, allowing consideration genotyped ungenotype...

The paper deals with the best unbiased estimators of the blocked compound symmetric covariance structure for m−variate observations over u sites under the assumption of multivariate normality. The free-coordinate approach is used to prove that the quadratic estimation of covariance parameters is equivalent to linear estimation with a properly defined inner product in the space of symmetric matr...

Following the Gauss-Markov theorem the generalized lest-squares estimator is the best linear unbiased estimator but following the kriging theory its use is limited. This paper shows the kriging constraint on the classic generalized least-squares estimator.

This paper surveys algorithms for generating unbiased random binary trees. There exist several linear time algorithms. The best algorithms use only integers of size On to generate binary trees on n nodes.