Computing the minimal efficiency of designs by a differentiable approximation of -optimality criteria.
The least squres invariant quadratic estimator of an unknown covariance function of a stochastic process is defined and a sufficient condition for consistency of this estimator is derived. The mean value of the observed process is assumed to fulfil a linear regresion model. A sufficient condition for consistency of the least squares estimator of the regression parameters is derived, too.
A robust version of the Ordinary Least Squares accommodating the idea of weighting the order statistics of the squared residuals (rather than directly the squares of residuals) is recalled and its properties are studied. The existence of solution of the corresponding extremal problem and the consistency under heteroscedasticity is proved.
We obtain conditions for L₂ and strong consistency of the least square estimators of the coefficients in a multi-linear regression model with a stationary random noise. For given non-random regressors, we obtain conditions which ensure L₂-consistency for all wide sense stationary noise sequences with spectral measure in a given class. The condition for the class of all noises with continuous (i.e., atomless) spectral measures yields also -consistency when the noise is strict sense stationary with...
The paper presents in a generalized form the problem of the geodetic network adjustment by the Helmert-Pranis Pranievich groups method (groups with junction points included or not). The adjustment problem, as well as the cofactor matrix derivation for the partial-independent and linkage unknowns, was completely formulated by transformed weight matrix definition and usage. A complete sequence of the computing stages for the geodetic networks divided into groups without junction points was given for...
In this paper we comment on some papers written by Jerzy K. Baksalary. In particular, we draw attention to the development process of some specific research ideas and papers now that some time, more than 15 years, has gone after their publication.
The following three results for the general multivariate Gauss-Markoff model with a singular covariance matrix are given or indicated. determinant ratios as products of independent chi-square distributions, moments for the determinants and the method of obtaining approximate densities of the determinants.
A method of geometrical characterization of multidimensional data sets, including construction of the convex hull of the data and calculation of the volume of the convex hull, is described. This technique, together with the concept of minimum convex hull volume, can be used for detection of influential points or outliers in multiple linear regression. An approximation to the true concept is achieved by ordering the data into a linear sequence such that the volume of the convex hull of the first...
L’effet d’un traitement sur une compétence peut être exprimé par le coefficient de régression partiel avec contrôle de la compétence initiale . Quand et sont mesurées avec erreurs par et , cet effet se manifeste par le coefficient dans la régression de sur et . Le biais entre et est explicité, discuté et montré systématique si et sont corrélés. L’importance de bien spécifier le modèle, dont une condition nécessaire et suffisante d’identification est donnée, est mise en...
The paper studies a new class of robust regression estimators based on the two-step least weighted squares (2S-LWS) estimator which employs data-adaptive weights determined from the empirical distribution or quantile functions of regression residuals obtained from an initial robust fit. Just like many existing two-step robust methods, the proposed 2S-LWS estimator preserves robust properties of the initial robust estimate. However, contrary to the existing methods, the first-order asymptotic behavior...