A minimum-entropy estimator for regression problems with unknown distribution of observation errors

Mathematics – Probability

Scientific paper

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Probability Theory, Information Theory And Communication Theory, Data Analysis: Algorithms And Implementation, Data Management

Scientific paper

We consider a nonlinear regression model, with independent observation errors identically distributed with an unknown probability density function f(.). Instead of minimizing the empirical version of the entropy of f(.) based on the residuals, which corresponds to maximum likelihood estimation and requires the knowledge of f(.), we minimize the entropy of a (symmetrized) kernel estimate fcircn,h of f(.), constructed from the residuals. Two examples are presented to illustrate the finite-sample behavior of this estimator (accuracy, robustness). Some (preliminary) consistency results are given. .

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