Minimum Distance Estimation
We introduce a new class of estimators — minimum distance estimators — and describe their properties in regular and nonstandard situations. These estimators, in the regular case of Hilbert metrics, are consistent and asymptotically normal. In nonstandard situations, their behavior is similar to the behavior of the MLE. We find that in certain circumstances these estimators are local asymptotic minimax (asymptotically optimal) and they are better than the MLE and BE. In the case of L1-norm and sup-norm the limit distributions of the estimators are non-Gaussian, but the limit (as T→ 0) distributions of these (limit) as ε→ 0 random variables are Gaussian.
KeywordsFunction Versus Gaussian Process Wiener Process Asymptotic Normality Regular Case
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