Abstract
Preserving the robustness of the procedure has, at the present time, become almost a default requirement for statistical data analysis. Since efficiency at the model and robustness under misspecification of the model are often in conflict, it is important to choose such inference procedures which provide the best compromise between these two concepts. Some minimum Bregman divergence estimators and related tests of hypothesis seem to be able to do well in this respect, with the procedures based on the density power divergence providing the existing standard. In this paper we propose a new family of Bregman divergences which is a superfamily encompassing the density power divergence. This paper describes the inference procedures resulting from this new family of divergences and makes a strong case for the utility of this divergence family in statistical inference.
Highlights
In statistical modeling, parameter estimation is an inevitable and formidable task
We have performed a simulation study to analyze the performance of the L Density Power Divergence (DPD) and the associated minimum distance estimators under the N(,1) model at a given level of contamination
In the following study data are generated from two normal mixtures, 0.9N(0,1) +0.1N(5,1) and 0.8N(0,1) +0.2N(5,1), where N(0,1) represents the target distribution and the second component is the contamination
Summary
Parameter estimation is an inevitable and formidable task. Accurate estimation of the model facilitates the characterization and the subsequent understanding of the mechanism that generates the observed data. Statistical distances can be useful tools for the estimation of the model parameters. Statistical distances can be naturally applied to the case of parametric statistical inference. The most important idea in parametric minimum distance inference is the quantification of the degree of closeness between the sample data and parametric model as a function of an unknown set of parameters through a suitable distance-like measure. The estimate of the parameter is obtained by minimizing this “distance” over the parameter space
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