Non-Parametric Maximum Likelihood Density Estimation and Simulation-Based Minimum Distance Estimators

Details Non-Parametric Maximum Likelihood Density Estimation and Simulation-Based Minimum Distance Estimators Non-Parametric Maximum Likelihood Density Estimation and Simulation-Based Minimum Distance Estimators

2010-12-17

arxiv.org/abs/1012.3851v2

Mathematical Methods of Statistics 20, 2011, 288-326

Mathematics

Statistics Theory

minor corrections, some discussion added, some material removed

Scientific paper

Indirect inference estimators (i.e., simulation-based minimum distance estimators) in a parametric model that are based on auxiliary non-parametric maximum likelihood density estimators are shown to be asymptotically normal. If the parametric model is correctly specified, it is furthermore shown that the asymptotic variance-covariance matrix equals the inverse of the Fisher-information matrix. These results are based on uniform-in-parameters convergence rates and a uniform-in-parameters Donsker-type theorem for non-parametric maximum likelihood density estimators.

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