Two-stage regression model
Uncertainty of coordinates and looking for dispersion of GPS receiver
The aim of the paper is to show some possible statistical solution of the estimation of the dispersion of the GPS receiver. The presented method (based on theory of linear model with additional constraints of type I) can serve for an improvement of the accuracy of estimators of coordinates acquired from the GPS receiver.
Uncertainty of the design and covariance matrices in linear statistical model
The aim of the paper is to determine an influence of uncertainties in design and covariance matrices on estimators in linear regression model.
Underparametrization of weakly nonlinear regression models
A large number of parameters in regression models can be serious obstacle for processing and interpretation of experimental data. One way how to overcome it is an elimination of some parameters. In some cases it need not deteriorate statistical properties of estimators of useful parameters and can help to interpret them. The problem is to find conditions which enable us to decide whether such favourable situation occurs.
Uniformly best linear-quadratic estimator in a special structure of the regression model.
Variance components and an additional experiment
Estimators of parameters of an investigated object can be considered after some time as insufficiently precise. Therefore, an additional measurement must be realized. A model of a measurement, taking into account both the original results and the new ones, has a litle more complicated covariance matrix, since the variance components occur in it. How to deal with them is the aim of the paper.
Variance components and nonlinearity
Unknown parameters of the covariance matrix (variance components) of the observation vector in regression models are an unpleasant obstacle in a construction of the best estimator of the unknown parameters of the mean value of the observation vector. Estimators of variance componets must be utilized and then it is difficult to obtain the distribution of the estimators of the mean value parameters. The situation is more complicated in the case of nonlinearity of the regression model. The aim of the...
Variance Estimation Using Auxiliary Information: An Almost Unbiased Multivariate Ratio Estimator.
Variance function estimation via model selection
The problem of estimating an unknown variance function in a random design Gaussian heteroscedastic regression model is considered. Both the regression function and the logarithm of the variance function are modelled by piecewise polynomials. A finite collection of such parametric models based on a family of partitions of support of an explanatory variable is studied. Penalized model selection criteria as well as post-model-selection estimates are introduced based on Maximum Likelihood (ML) and Restricted...
Variance of Plug-in Estimators in Multivariate Regression Models
Variance components in regression models are usually unknown. They must be estimated and it leads to a construction of plug–in estimators of the parameters of the mean value of the observation matrix. Uncertainty of the estimators of the variance components enlarge the variances of the plug–in estimators. The aim of the paper is to find this enlargement.
Weak -consistency of the least weighted squares under heteroscedasticity
Weak nonlinearity of growth curve models
Асимптотическое поведение статистических оценок параметров многомерной разрывной плотности
Лекции по теории оценивания многих параметров
Моменты отклонений оценки подстановки и ее кусочно-гладких аппроксимаций.
Некоторые асимптотические результаты, связанные с критерием Шовенэ для многомерных случайных величин
Характеризация функций потерь в статистической теории оценивания