The linear regression model in which the vector of the first order parameter is divided into two parts: to the vector of the useful parameters and to the vector of the nuisance parameters is considered. The type I constraints are given on the useful parameters. We examine eliminating transformations which eliminate the nuisance parameters without loss of information on the useful parameters.
En el presente trabajo se realiza un estudio de la envoltura convexa de una muestra normal bivariante, analizando la distribución de la pendiente de sus aristas. En base a ello se propone un estimador del coeficiente de correlación de la población, investigando algunas propiedades del mismo.
This paper is a continuation of the paper [6]. It dealt with parameter estimation in connecting two–stage measurements with constraints of type I. Unlike the paper [6], the current paper is concerned with a model with additional constraints of type II binding parameters of both stages. The article is devoted primarily to the computational aspects of algorithms published in [5] and its aim is to show the power of -optimum estimators. The aim of the paper is to contribute to a numerical solution...
The paper deals with an optimal estimation of the quadratic function , where is a known matrix, in the model . The distribution of is assumed to be symmetric and to have a finite fourth moment. An explicit form of the best unbiased estimator is given for a special case of the matrix .
Dispersion of measurement results is an important parameter that enables us not only to characterize not only accuracy of measurement but enables us also to construct confidence regions and to test statistical hypotheses. In nonlinear regression model the estimator of dispersion is influenced by a curvature of the manifold of the mean value of the observation vector. The aim of the paper is to find the way how to determine a tolerable level of this curvature.
Statistical inference procedures based on least absolute deviations involve estimates of a matrix which plays the role of a multivariate nuisance parameter. To estimate this matrix, we use kernel smoothing. We show consistency and obtain bounds on the rate of convergence.
This paper concerns the estimation of the parameters that describe spherical invariant stable distributions: the index α ∈ (0,2] and the scale parameter σ >0. We present a kind of moment estimators derived from specially transformed original data.
The paper deals with the estimation of unknown vector parameter of mean and scalar parameters of variance as well in two-stage linear model, which is a special type of mixed linear model. The necessary and sufficient condition for the existence of uniformly best unbiased estimator of parameter of means is given. The explicite formulas for these estimators and for the estimators of the parameters of variance as well are derived.
The linear regression model, where the mean value parameters are divided into stable and nonstable part in each of both epochs of measurement, is considered in this paper. Then, equivalent formulas of the best linear unbiased estimators of this parameters in both epochs using partitioned matrix inverse are derived.
The aim of the paper is estimation of the generalized variance of a bivariate normal distribution in the case of a sample with missing observations. The estimator based on all available observations is compared with the estimator based only on complete pairs of observations.
In this paper the Kronecker and inner products of mean vectorsof two different populations are considered. Using the generalized jackknife approach, estimators for these products are constructed which turn out to be unbiased, provided one can assume multinormal distribution.
The main aim is to estimate the noncentrality matrix of a noncentral Wishart distribution. The method used is Leung's but generalized to a matrix loss function. Parallelly Leung's scalar noncentral Wishart identity is generalized to become a matrix identity. The concept of Löwner partial ordering of symmetric matrices is used.