Randomized goodness of fit tests

Friedrich Liese; Bing Liu

doi:10.18453/rosdok_id00005830

zum übergeordneten Dokument

Friedrich Liese Bing Liu

Randomized goodness of fit tests

University of Rostock, Institute of Mathematics, 2009

https://doi.org/10.18453/rosdok_id00005830

Abstract: Goodness of fi…t tests based on the empirical distribution function fail to be asymptotically distribution free if parameters are estimated. Asymptotically, the empirical process with estimated parameters is a centered Gaussian process with a covariance that di¤ers from the covariance function of the Brownian bridge. If the maximum likelihood estimator is used then the new covariance function is smaller, in the Loewner semiorder, than the covariance function of the Brownian bridge. Therefore one may transform the empirical process with estimated parameters back to a Brownian bridge by adding an independent process that is suitably constructed. Classical goodness of …t statistics have aftzer this transformation an asymptotic distribution as in the case of known parameters. The power under local alternatives of this new goodness of fit tests is studied and computer simulations compare the new test with their bootstrap versions.

Workingpaper Freier Zugang

Titel:

Randomized goodness of fit tests

Schriftenreihe:

Preprints aus dem Institut für Mathematik, 09/1

Beteiligte Personen:

Friedrich Liese[VerfasserIn]
	140883363
Bing Liu[VerfasserIn]
	102958561X

Zusammenfassung:

Goodness of fi…t tests based on the empirical distribution function fail to be asymptotically distribution free if parameters are estimated. Asymptotically, the empirical process with estimated parameters is a centered Gaussian process with a covariance that di¤ers from the covariance function of the Brownian bridge. If the maximum likelihood estimator is used then the new covariance function is smaller, in the Loewner semiorder, than the covariance function of the Brownian bridge. Therefore one may transform the empirical process with estimated parameters back to a Brownian bridge by adding an independent process that is suitably constructed. Classical goodness of …t statistics have aftzer this transformation an asymptotic distribution as in the case of known parameters. The power under local alternatives of this new goodness of fit tests is studied and computer simulations compare the new test with their bootstrap versions. [Englisch]

Dokumenttyp:

Workingpaper

Einrichtung:

Mathematisch-Naturwissenschaftliche Fakultät

Sprache:

Englisch

Sachgruppe der DNB:

510 Mathematik

Umfang:

1 Online-Ressource (28 Seiten)

Veröffentlichung /
Entstehung:

Rostock: University of Rostock, Institute of Mathematics