Nonsensitiveness regions for threshold ellipsoids
The problem is to determine nonsensitiveness regions for threshold ellipsoids within a regular mixed linear model.
Nonsensitiveness regions in universal models
Note on inappropriate trend and seasonal elimination
Note on the ANOVA of a completely confounded factorial experiment
The purpose of this paper is to present a modern approach to the analysis of variance (ANOVA) of disconnected resolvable group divisible partially balanced incomplete block (GDPBIB) designs with factorial structure and with some interaction effects completely confounded. A characterization of a factorial experiment with completely confounded interaction is given. The treatment effect estimators and some relations between the matrix F of the reduced normal equations and the information matrix A are...
Note on the estimation of parameters of the mean and the variance in -stage linear models
The paper deals with the estimation of the unknown vector parameter of the mean and the parameters of the variance in the general -stage linear model. Necessary and sufficient conditions for the existence of the uniformly minimum variance unbiased estimator (UMVUE) of the mean-parameter under the condition of normality are given. The commonly used least squares estimators are used to derive the expressions of UMVUE-s in a simple form.
Numerical experiments with least squares spline estimators in a parametric regression model.
On a distance between estimable functions.
In this paper we study the main properties of a distance introduced by C.M. Cuadras (1974). This distance is a generalization of the well-known Mahalanobis distance between populations to a distance between parametric estimable functions inside the multivariate analysis of variance model. Reduction of dimension properties, invariant properties under linear automorphisms, estimation of the distance, distribution under normality as well as the interpretation as a geodesic distance are studied and...
On a generalization of the orthogonal regression
On a hybrid experimental design
On a linearization of regression models
An approximate value of a parameter in a nonlinear regression model is known in many cases. In such situation a linearization of the model is possible however it is important to recognize, whether the difference between the actual value of the parameter and the approximate value does not cause significant changes, e.g., in the bias of the estimator or in its variance, etc. Some rules suitable for a solution of this problem are given in the paper.
On adaptive estimation in nonlinear regression
On admissibility of linear estimators in models with finitely generated parameter space
The paper refers to the research on the characterization of admissible estimators initiated by Cohen [2]. In our paper it is proved that for linear models with finitely generated parameter space the limit of a sequence of the unique locally best linear estimators is admissible. This result is used to give a characterization of admissible linear estimators of fixed and random effects in a random linear model for spatially located sensors measuring intensity of a source of signals in discrete instants...
On an accuracy of change points
On Classes of Estimators of the Variance Function of a Linear Estimator.
On concepts and measures of bivariate stochastic dependence
On conditional independence and log-convexity
If conditional independence constraints define a family of positive distributions that is log-convex then this family turns out to be a Markov model over an undirected graph. This is proved for the distributions on products of finite sets and for the regular Gaussian ones. As a consequence, the assertion known as Brook factorization theorem, Hammersley–Clifford theorem or Gibbs–Markov equivalence is obtained.
On eliminating transformations for nuisance parameters in multivariate linear model
The multivariate linear model, in which the matrix of the first order parameters is divided into two matrices: to the matrix of the useful parameters and to the matrix of the nuisance parameters, is considered. We examine eliminating transformations which eliminate the nuisance parameters without loss of information on the useful parameters and on the variance components.
On empirical Bayes estimation of multivariate regression coefficient.
On equivalence problem in linear regression models. I. BLUE of the mean value
There exist many different ways of determining the best linear unbiased estimation of regression coefficients in general regression model. In Part I of this article it is shown that all these ways are numerically equivalent almost everyvhere. In Part II conditions are considered under which all the unbiased estimations of the unknown covariance matrix scalar factor are numerically equivalent almost everywhere.
On equivalence problem in linear regression models. II. Unbiased estimation of the covariance matrix scalar factor
There exist many different ways of determining the best linear unbiased estimation of regression coefficients in general regression model. In Part I of this article it is shown that all these ways are numerically equivalent almost everyvhere. In Part II conditions are considered under which all the unbiased estimations of the unknown covariance matrix scalar factor are numerically equivalent almost everywhere.