Semiparametric Testing of Statistical Functionals Revisited
16 Pages Posted: 1 Jul 2013
Date Written: March 30, 2012
Abstract Along the lines of Janssen's and Pfanzagl's work the testing theory for statistical functionals is further developed for non-parametric one-sample problems. Efficient tests for the one-sided and two-sided problems are derived for nonparametric statistical functionals. The asymptotic power function is calculated under implicit alternatives and hypotheses, which are given by the functional itself, for the one-sided and two-sided cases. Under mild regularity assumptions is shown that these tests are asymptotic most powerful. The combination of the modern theory of Le Cam and approximation in limit experiments provide a deep insight into the upper bounds for asymptotic power functions tests for the one-sided and two-sided problems of hypothesis testing. As example tests concerning the von Mises functional are treated in nonparametric context.
Keywords: statistics, semiparametric, testing, functional, differntiable, asymptotic, optimal
JEL Classification: G00, A00
Suggested Citation: Suggested Citation