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http://hdl.handle.net/1942/34674
Title: | Bootstrap based goodness-of-fit tests for binary multivariate regression models | Authors: | VAN HEEL, Mareike Dikta, Gerhard BRAEKERS, Roel |
Issue Date: | 2021 | Publisher: | SPRINGER HEIDELBERG | Source: | Journal of the Korean Statistical Society, | 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. 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. |
Notes: | van Heel, M (corresponding author), Fachhsch Aachen, D-52428 Julich, Germany.; van Heel, M (corresponding author), Univ Hasselt, B-3500 Hasselt, Belgium. van-heel@fh-aachen.de; dikta@fh-aachen.de; roel.braekers@uhasselt.be |
Keywords: | Binary regression model; Bootstrap based test; Goodness-of-fit test;;Marked empirical process | Document URI: | http://hdl.handle.net/1942/34674 | ISSN: | 1226-3192 | e-ISSN: | 2005-2863 | DOI: | 10.1007/s42952-021-00142-4 | ISI #: | WOS:000681182000001 | Rights: | © The Author(s) 2021 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2022 |
Appears in Collections: | Research publications |
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File | Description | Size | Format | |
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VanHeel2021_Article_BootstrapBasedGoodness-of-fitT.pdf | Published version | 2.17 MB | Adobe PDF | View/Open |
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