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A note on robust estimation in logistic regression model

Tadeusz Bednarski (2016)

Discussiones Mathematicae Probability and Statistics

Computationally attractive Fisher consistent robust estimation methods based on adaptive explanatory variables trimming are proposed for the logistic regression model. Results of a Monte Carlo experiment and a real data analysis show its good behavior for moderate sample sizes. The method is applicable when some distributional information about explanatory variables is available.

Blended φ -divergences with examples

Václav Kůs (2003)


Several new examples of divergences emerged in the recent literature called blended divergences. Mostly these examples are constructed by the modification or parametrization of the old well-known phi-divergences. Newly introduced parameter is often called blending parameter. In this paper we present compact theory of blended divergences which provides us with a generally applicable method for finding new classes of divergences containing any two divergences D 0 and D 1 given in advance. Several examples...

Challenging the empirical mean and empirical variance: A deviation study

Olivier Catoni (2012)

Annales de l'I.H.P. Probabilités et statistiques

We present new M-estimators of the mean and variance of real valued random variables, based on PAC-Bayes bounds. We analyze the non-asymptotic minimax properties of the deviations of those estimators for sample distributions having either a bounded variance or a bounded variance and a bounded kurtosis. Under those weak hypotheses, allowing for heavy-tailed distributions, we show that the worst case deviations of the empirical mean are suboptimal. We prove indeed that for any confidence level, there...

Computational aspects of robust Holt-Winters smoothing based on M -estimation

Christophe Croux, Sarah Gelper, Roland Fried (2008)

Applications of Mathematics

To obtain a robust version of exponential and Holt-Winters smoothing the idea of M -estimation can be used. The difficulty is the formulation of an easy-to-use recursive formula for its computation. A first attempt was made by Cipra (Robust exponential smoothing, J. Forecast. 11 (1992), 57–69). The recursive formulation presented there, however, is unstable. In this paper, a new recursive computing scheme is proposed. A simulation study illustrates that the new recursions result in smaller forecast...

Concept of Data Depth and Its Applications

Ondřej Vencálek (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Data depth is an important concept of nonparametric approach to multivariate data analysis. The main aim of the paper is to review possible applications of the data depth, including outlier detection, robust and affine-equivariant estimates of location, rank tests for multivariate scale difference, control charts for multivariate processes, and depth-based classifiers solving discrimination problem.

Funcionales de mínima g-divergencia y sus estimadores asociados (II).

Francisco Javier Cano Sevilla, M.ª Pilar Lasala Calleja (1984)

Trabajos de Estadística e Investigación Operativa

Se realizan dos estudios de simulación para comprobar el comportamiento asintóticamente robusto del estimador de mínima g-divergencia para dos elecciones notables de la función g.

Funcionales de mínima g-divergencia y sus estimadores asociados (I).

Francisco José Cano Sevilla, M.ª Pilar Lasala Calleja (1984)

Trabajos de Estadística e Investigación Operativa

Se introducen los funcionales de mínima g-divergencia y sus estimadores asociados. Se prueba la existencia y robustez del funcional y la convergencia del estimador asociado.

Graphical display in outlier diagnostics; adequacy and robustness.

Nethal K. Jajo (2005)


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.

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