Estimation of the variance components in the linear regression model
Estimation of variance components in mixed linear models
The MINQUE of the linear function of the unknown variance-components parameter in mixed linear model under linear restrictions of the type is defined and derived. As an illustration of this estimator the example of the one-way classification model with the restrictions , where , is given.
Estimation récursive des paramètres d'un modèle de régression, variant au cours du temps
Estimation Under Linear Regression Models.
Estimator selection in the gaussian setting
We consider the problem of estimating the mean of a Gaussian vector with independent components of common unknown variance . Our estimation procedure is based on estimator selection. More precisely, we start with an arbitrary and possibly infinite collection of estimators of based on and, with the same data , aim at selecting an estimator among with the smallest Euclidean risk. No assumptions on the estimators are made and their dependencies with respect to may be unknown. We establish...
Estimators for epidemic alternatives
We introduce and study the behavior of estimators of changes in the mean value of a sequence of independent random variables in the case of so called epidemic alternatives which is one of the variants of the change point problem. The consistency and the limit distribution of the estimators developed for this situation are shown. Moreover, the classical estimators used for `at most change' are examined for the studied situation.
Exact distributions in the model of a regression line for the threshold parameter with exponential distribution of errors
In this paper it is shown how one can work out exact distributions of estimators and test statistics in the model of a regression line for the threshold parameter with exponential distribution of errors. This is done on a test statistics which is related to a problem of Zvára [Zvara95].
Exponential regression
Extensions of the Frisch-Waugh-Lovell Theorem
In this paper we introduce extensions of the so-called Frisch-Waugh-Lovell Theorem. This is done by employing the close relationship between the concept of linear sufficiency and the appropriate reduction of linear models. Some specific reduced models which demonstrate alternatives to the Frisch-Waugh-Lovell procedure are discussed.
Ferrero formula and triangle misclosures revisited
Finding an ε-optimal regression subset
Fitting a linear regression model by combining least squares and least absolute value estimation.
Robust estimation of the multiple regression is modeled by using a convex combination of Least Squares and Least Absolute Value criterions. A Bicriterion Parametric algorithm is developed for computing the corresponding estimates. The proposed procedure should be specially useful when outliers are expected. Its behavior is analyzed using some examples.
Fixed precision estimation of the parameters of a linear regression model with unknown covariance structure
From equivalent linear equations to Gauss-Markov theorem.
Gaussian model selection
Our purpose in this paper is to provide a general approach to model selection via penalization for Gaussian regression and to develop our point of view about this subject. The advantage and importance of model selection come from the fact that it provides a suitable approach to many different types of problems, starting from model selection per se (among a family of parametric models, which one is more suitable for the data at hand), which includes for instance variable selection in regression models,...
Generalized linear estimate of functions of random matrix arguments
Generalized method of least squares collocation
Two general solutions of the collocation problem of physical geodesy are given. Their mutual equivalency and equivalency of them to the classical solution in the regular case are proved. The regularity means the non-singularity of the covariance matrix of those random variables by outcomes of which the measured values of the gravitational field are generated.
Goodness of fit procedures for the multivariate linear model based on spherical harmonics.
Goodness-of-fit tests for parametric regression models based on empirical characteristic functions
Test procedures are constructed for testing the goodness-of-fit in parametric regression models. The test statistic is in the form of an L2 distance between the empirical characteristic function of the residuals in a parametric regression fit and the corresponding empirical characteristic function of the residuals in a non-parametric regression fit. The asymptotic null distribution as well as the behavior of the test statistic under contiguous alternatives is investigated. Theoretical results are...
Graphical display in outlier diagnostics; adequacy and robustness.
Outlier robust diagnostics (graphically) using Robustly Studentized Robust Residuals (RSRR) and Partial Robustly Studentized Robust Residuals (PRSRR) are established. One problem with some robust residual plots is that the residuals retain information from certain predicated values (Velilla, 1998). The RSRR and PRSRR techniques are unaffected by this complication and as a result they provide more interpretable results.