The aim of the paper is to derive for the negative correlation function with a time parameter an asymptotic disjunction limj→∞ ωi jvi of the numerical generalized least-squares estimator ωi jvi of an unknown constant mean of random field in fact the correct classic generalized least-squares estimator of an unknown constant mean of the field.

In 1922 R. A. Fisher introduced the modern regression model, synthesizing the regression theory of Pearson and Yule and the least squares theory of Gauss. The innovation was based on Fisher’s realization that the distribution associated with the regression coefficient was unaffected by the distribution of X. Subsequently Fisher interpreted the fixed X assumption in terms of his notion of ancill...

By using the complex representation of quaternion matrices, the Moore–Penrose generalized inverse and the Kronecker product of matrices, the expressions of the least squares η-Hermitian solution with the least norm and the expressions of the least squares η-anti-Hermitian solution with the least norm are derived for the matrix equation AXB+CXD = E over quaternions.

This work studies the phenomenon of heteroscedasticity and its consequences for various methods of linear regression, including the least squares, least weighted squares and regression quantiles. We focus on hypothesis tests for these regression methods. The new approach consists in deriving asymptotic heteroscedasticity tests for robust regression, which are asymptotically equivalent to standa...

In this paper, we examine rst and second order asymptotic theory for two estima-tors in a linear quantile model in the case where the response is observed multiple times at xed covariate vectors x 1 ; ; x k. The rst estimator is the regression quantile esti-mator introduced by Koenker and Bassett (1978) while the second estimator is a least squares estimator on the sample quantiles of the respo...

A linear geostatistical model is considered. Properties of a universal kriging are studied when the locations of observations are measured with errors. Alternative prediction procedures are introduced and their least squares errors are analyzed.

Several extensions of the total least squares (TIS) method that are able to calculate a structured rank deficient approximation of a data matrix have been developed recently. The main result of this correspondence is the demonstration of the equivalence of two of these approaches, namely, the constrained total least squares (CTLS) approach and the structured total least squares (STLS) approach....