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**Bootstrap based goodness-of-fit tests for binary multivariate regression models.**
*(English)*
Zbl 1485.62102

Summary: 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 W. Stute [Ann. Stat. 25, No. 2, 613–641 (1997; Zbl 0926.62035)]. In contrast to W. Stute and L.-X. Zhu’s approach [Scand. J. Stat. 29, No. 3, 535–545 (2002; Zbl 1035.62073)], 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 and Zhu [loc. cit.], the simulations indicate a slightly improved power of the MBB based method. Finally, both methods are applied to a real data set.

### MSC:

62J12 | Generalized linear models (logistic models) |

62G10 | Nonparametric hypothesis testing |

62E20 | Asymptotic distribution theory in statistics |

### Keywords:

binary regression model; bootstrap based test; goodness-of-fit test; marked empirical process
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\textit{M. van Heel} et al., J. Korean Stat. Soc. 51, No. 1, 308--335 (2022; Zbl 1485.62102)

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