THE SECOND ORDER OPTIMALITY OF TESTS AND ESTIMATORS FOR
MINIMUM CONTRAST FUNCTIONALS. I
Abstract: The concept of is introduced. It is
shown that certain statistical procedures (asymptotically similar tests, asymptotically
similar confidence procedures and asymptotically median unbiased estimators)
derived from the minimum contrast estimators are 2nd order efficient, provided
the family of probability measures is rich enough to contain, together with each
probability measure, contiguous probability measures which are asymptotically ”least
favorable”. The 2nd order efficiency of statistical procedures based on the maximum
likelihood estimator follows by application of these results to parametric families of
probability measures. The results are valid only for ”continuous” probability measures.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -