Bootstrap based goodness-of-fit tests for binary multivariate regression models

Journal of the Korean Statistical Society, vol. 51, pp. 308–335

Abstract

Abstract We consider a binary multivariate regression model where the conditional expectation of a binary variable given a higher-dimensional input variable belongs to a parametric family. Based on this, we introduce a model-based bootstrap (MBB) for higher-dimensional input variables. This test can be used to check whether a sequence of independent and identically distributed observations belongs to such a parametric family. The approach is based on the empirical residual process introduced by Stute (Ann Statist 25:613–641, 1997). In contrast to Stute and Zhu’s approach (2002) Stute & Zhu (Scandinavian J Statist 29:535–545, 2002), a transformation is not required. Thus, any problems associated with non-parametric regression estimation are avoided. As a result, the MBB method is much easier for users to implement. To illustrate the power of the MBB based tests, a small simulation study is performed. Compared to the approach of Stute & Zhu (Scandinavian J Statist 29:535–545, 2002), the simulations indicate a slightly improved power of the MBB based method. Finally, both methods are applied to a real data set.

Authors 3

1. Mareike van Heel corresponding Aachen Fachhochschule Aachen

   FH Aachen · Hasselt University

   Affiliation as printed

   Fachhochschule Aachen, D-52428, Jülich, Germany

   Universiteit Hasselt, B-3500, Hasselt, Belgium

2. Gerhard Dikta Aachen Fachhochschule Aachen

   FH Aachen

   Affiliation as printed

   Fachhochschule Aachen, D-52428, Jülich, Germany

3. Roel Braekers

   Hasselt University

   Affiliation as printed

   Data Science Institute, I-Biostat, Universiteit Hasselt, B-3500, Hasselt, Belgium