Uniform law of large numbers and consistency of estimators for Harris diffusions

D. Loukianova and O. Loukianov

Statistics & Probability Letters, 2005, vol. 74, issue 4, 347-355

Abstract: Consider a family of local martingales depending on a parameter [theta] running through some compact in . We show that if their quadratic variations are Hölder in [theta], then the family satisfies a uniform law of large numbers. We apply it to deduce the almost sure consistency of maximum likelihood estimators for drift parameters of a multidimensional Harris recurrent diffusion, thereby extending a recent result of J.H. van Zanten for one-dimensional ergodic diffusions.

Keywords: Uniform; law; of; large; numbers; Harris; diffusion; Maximum; likelihood; estimator (search for similar items in EconPapers)
Date: 2005
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