Robust and Efficient Estimation by Minimising a Density Power Divergence

Robust and Efficient Estimation by Minimising a Density Power Divergence

| AYANENDRANATH BASU, IAN R. HARRIS, NILS L. HJORT, AND M. C. JONES
The paper introduces a new family of density-based divergence measures called density power divergences, which are indexed by a single parameter \(\alpha\). These divergences provide a robust extension of maximum likelihood estimation, offering a trade-off between robustness and efficiency. The method avoids the need for nonparametric density estimation and bandwidth selection, making it more practical than existing density-based minimum divergence methods. The authors derive the asymptotic properties of the estimators, including their consistency and asymptotic normality, and provide a robust model selection criterion. They also investigate the efficiency and breakdown properties of the estimators in various parametric families, demonstrating that the method retains high efficiency even for small values of \(\alpha\). Examples from normal and Poisson distributions, as well as real-world data sets, illustrate the robustness and efficiency of the proposed method. The paper also extends the density power divergence approach to regression models, providing a robust estimation method and discussing its large-sample behavior.The paper introduces a new family of density-based divergence measures called density power divergences, which are indexed by a single parameter \(\alpha\). These divergences provide a robust extension of maximum likelihood estimation, offering a trade-off between robustness and efficiency. The method avoids the need for nonparametric density estimation and bandwidth selection, making it more practical than existing density-based minimum divergence methods. The authors derive the asymptotic properties of the estimators, including their consistency and asymptotic normality, and provide a robust model selection criterion. They also investigate the efficiency and breakdown properties of the estimators in various parametric families, demonstrating that the method retains high efficiency even for small values of \(\alpha\). Examples from normal and Poisson distributions, as well as real-world data sets, illustrate the robustness and efficiency of the proposed method. The paper also extends the density power divergence approach to regression models, providing a robust estimation method and discussing its large-sample behavior.
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