Semiparametric Testing of Statistical Functionals Revisited

16 Pages Posted: 1 Jul 2013

Date Written: March 30, 2012

Abstract

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

Ostrovski, Vladimir, Semiparametric Testing of Statistical Functionals Revisited (March 30, 2012). Available at SSRN: https://ssrn.com/abstract=2287633 or http://dx.doi.org/10.2139/ssrn.2287633

Vladimir Ostrovski (Contact Author)

Talanx Asset Management ( email )

Charles-de-Gaulle-Platz 1
Cologne, DE NRW 50679
Germany

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