Testing Equivalence to Families of Multinomial Distributions with Application to the Independence Model

Statistics & Probability Letters, Volume 139, August 2018, Pages 61-66

10 Pages Posted: 7 May 2018 Last revised: 5 Jul 2019

Date Written: April 19, 2018

Abstract

We introduce efficient tests for equivalence to families of multinomial distributions. Asymptotic distribution of the test statistic is derived and the local asymptotic optimality of proposed tests is shown.

The finite sample performance of tests is improved by means of the parametric bootstrap. In order to make the bootstrap computationally feasible we introduce an efficient and consistent estimator of the boundary points. The asymptotic consistence and optimality of bootstrap based tests is proven.

We apply proposed equivalence tests to the independence model of two-way contingency tables. The finite sample performance is studied by Monte Carlo simulation. Finally we apply tests to real data sets.

The tests are initially implemented in VB.NET and available on GitHub, see github.com/TestingEquivalence/ApproximateIndependence. All simulations results in this paper are based on this VB.NET code.

More recently, the tests are improved and implemented in R, see github.com/TestingEquivalence/EquivalenceProductFamilieR.

Keywords: Equivalence, Testing, Multinomial, Collapsible, Independence, Contingency, Approximate

JEL Classification: C00, C02

Suggested Citation

Ostrovski, Vladimir, Testing Equivalence to Families of Multinomial Distributions with Application to the Independence Model (April 19, 2018). Statistics & Probability Letters, Volume 139, August 2018, Pages 61-66, Available at SSRN: https://ssrn.com/abstract=3165618

Vladimir Ostrovski (Contact Author)

Talanx Asset Management ( email )

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

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