Computing the minimal efficiency of designs by a differentiable approximation of -optimality criteria.
Confidence band for regression line with exponential distribution of errors
Confidence regions in a multivariate regression model with constraints II
Consistency in the p-th mean of the least Squares Estimators in Linear Models
Consistency of an estimate in linear regression with non-negative errors
Consistency of linear and quadratic least squares estimators in regression models with covariance stationary errors
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.
Consistency of the least weighted squares under heteroscedasticity
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.
Consistency of the LSE in Linear regression with stationary noise
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...
Consistent Estimation of a Regression with Errors in the Variables.
Contribuciones a la generalización del problema de compensación por grupos de Helmert-Pranis Pranievich.
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...
Corrections of estimators in linearized models
Covariance matrix elements estimation: special linear model without and with repeated measurement
Criterion for an approximation of variance components in regression models
Data imputation in switchback designs using a mixed model with correlated errors.
Decomposing matrices with Jerzy K. Baksalary
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.
Densities of determinant ratios, their moments and some simultaneous confidence intervals in the multivariate Gauss-Markoff model
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.
Detection of influential points by convex hull volume minimization
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...
Different kinds of sufficiency in the general Gauss-Markov model
Effet des erreurs de mesure sur l'évaluation de l'efficacité d'un traitement
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...
Efficient robust estimation of time-series regression models
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...