Die messende Prüfung bei Abweichung von der Normalverteilungsannahme.
Discriminability of robust test under heavy contamination
Efficiency and robustness control via distorted maximum likelihood estimation
Efficiency rate and local deficiency of Huber's location estimators and of the α-estimators.
The paper studies the problem of selecting an estimator with (approximately) minimal asymptotic variance. For every fixed contamination level there is usually just one such estimator in the considered family. Using the first and the second derivative of the asymptotic variance with respect to the parameter which parametrizes the family of estimators the paper gives two examples of how to select the estimator and gives an approximation to a loss which we suffer when we use the estimator with approximately...
Efficiency rate and local deficiency of the most powerful tests in the model of contaminacy with general neighbourhoods
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...
Estimating the contamination level of data in the framework of linear regression analysis.
An estimator of the contamination level of data is proposed in the framework of linear models and its asymptotic behavior is investigated. A numerical study illustrates its finite sample performance under an alternative.
Estimation of contamination level in model of contaminacy with general neighbourhoods
Estimators, escort probabilities, and -exponential families in statistical physics.
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.
Generalized Bayesian-type estimators. Robust and sensitivity analysis
Hypothesis Testing and Parameter Estimation Based on M-Statistics in k Samples with Unequal Variances.
Identification with interruptions as an anti-bursting device
Influence of contamination level deviations on the test error probabilities
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...
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...
Large adaptive estimation in linear regression model. I. Consistency
Les estimateurs robustes sont-ils vraiment robustes en pratique ?
-estimators of structural parameters in pseudolinear models
Real valued -estimators in a statistical model with observations are replaced by -valued -estimators in a new model with observations , where are regressors, is a structural parameter and a structural function of the new model. Sufficient conditions for the consistency of are derived, motivated by the sufficiency conditions for the simpler “parent estimator” . The result is a general method of consistent estimation in a class of nonlinear (pseudolinear) statistical problems. If...
Mean-square-error-robustness of linear estimates in the exponential model