ABSTRACT - On the Heuristics of Statistical Results.
Adaptive maximum-likelihood-like estimation in linear models. I. Consistency
On second order efficiency of a robust test and approximations of its error probabilities
Adaptive estimation in linear regression model. II. Asymptotic normality
Influence of contamination level deviations on the test error probabilities
On the continuity of the minimal -entropy
Large adaptive estimation in linear regression model. I. Consistency
Asymptotic behaviour of the likelihood ratio test under presence of deviations of the model
Adaptive maximum-likelihood-like estimation in linear models. II. Asymptotic normality
Asymptotic behaviour of the robust test in the Rieder's model of contamination
Estimation of contamination level in model of contaminacy with general neighbourhoods
Efficiency rate and local deficiency of the most powerful tests in the model of contaminacy with general neighbourhoods
Combining forecasts using the least trimmed squares
Employing recently derived asymptotic representation of the least trimmed squares estimator, the combinations of the forecasts with constraints are studied. Under assumption of unbiasedness of individual forecasts it is shown that the combination without intercept and with constraint imposed on the estimate of regression coefficients that they sum to one, is better than others. A numerical example is included to support theoretical conclusions.
The least trimmed squares. Part III: Asymptotic normality
Asymptotic normality of the least trimmed squares estimator is proved under general conditions. At the end of paper a discussion of applicability of the estimator (including the discussion of algorithm for its evaluation) is offered.
The least trimmed squares. Part I: Consistency
The consistency of the least trimmed squares estimator (see Rousseeuw [Rous] or Hampel et al. [HamRonRouSta]) is proved under general conditions. The assumptions employed in paper are discussed in details to clarify the consequences for the applications.
The least trimmed squares. Part II: -consistency
-consistency of the least trimmed squares estimator is proved under general conditions. The proof is based on deriving the asymptotic linearity of normal equations.
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.
Instrumental weighted variables under heteroscedasticity. Part II – Numerical study
Results of a numerical study of the behavior of the instrumental weighted variables estimator – in a competition with two other estimators – are presented. The study was performed under various frameworks (homoscedsticity/heteroscedasticity, several level and types of contamination of data, fulfilled/broken orthogonality condition). At the beginning the optimal values of eligible parameters of estimatros in question were empirically established. It was done under the various sizes of data sets and...
Instrumental weighted variables under heteroscedasticity. Part I – Consistency
The proof of consistency instrumental weighted variables, the robust version of the classical instrumental variables is given. It is proved that all solutions of the corresponding normal equations are contained, with high probability, in a ball, the radius of which can be selected - asymptotically - arbitrarily small. Then also -consistency is proved. An extended numerical study (the Part II of the paper) offers a picture of behavior of the estimator for finite samples under various types and levels...
On properties of binary random numbers
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