Confidence regions in nonlinear models with constraints
Confidence regions in nonlinear regression models
New curvature measures for nonlinear regression models are developed and methods of their computing are given. Using these measures, more accurate confidence regions for parameters than those based on linear or quadratic approximations are obtained.
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 least squares estimates in a system of linear correlation models [Book]
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
Covariance Structure of Principal Components for Three-Part Compositional Data
Statistical analysis of compositional data, multivariate observations carrying only relative information (proportions, percentages), should be performed only in orthonormal coordinates with respect to the Aitchison geometry on the simplex. In case of three-part compositions it is possible to decompose the covariance structure of the well-known principal components using variances of log-ratios of the original parts. They seem to be helpful for the interpretation of these special orthonormal coordinates....
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...
Deux méthodes linéaires en statistique multidimensionnelle (1). A. - Introduction aux deux méthodes. B. - Analyse en composantes principales
Dans deux articles, dont voici le premier, sont présentés deux exemples d'analyse statistique par des méthodes factorielles. Le cadre mathématique de l'exposé est algébrique. La présente formulation de ces problèmes s'appuie sur l'expérience d'enseignement menée à l'UER de Mathématiques, Logique Formelle et Informatique de l'Université René-Descartes, ainsi que sur une rédaction parue dans les actes du Colloque «Analyse des données en architecture et urbanisme» [5].
Deux structures statistiques fondamentales en analyse de la variance univariée et multivariée