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Asymptotic Normality of the Minimum Non-Hilbertian Distance Estimators for a Diffusion Process with Small Noise

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Abstract

A one-dimensional diffusion type process with small noise is observed up to the time T. It depends on an unknown real parameter. Some minimum distance estimators of this parameter are considered. These estimators are defined using the L p-metric or the uniform metric. The limiting distribution of the normalizing minimum distance estimators (as the noise vanishing) is known to be the distribution of a random variable. The distribution of this random variable is studied as the time T goes to the infinity. We will prove under some conditions that it has a limiting Gaussian law.

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Authors
  1. Christophe Aubry
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Aubry, C. Asymptotic Normality of the Minimum Non-Hilbertian Distance Estimators for a Diffusion Process with Small Noise. Statistical Inference for Stochastic Processes 2, 175–194 (1999). https://doi.org/10.1023/A:1009999627569

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