On Second order correctness of Bootstrap in Logistic Regression Article Swipe
Debraj Das
,
Priyam Das
·
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2007.01615
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2007.01615
In the fields of clinical trials, biomedical surveys, marketing, banking, with dichotomous response variable, the logistic regression is considered as an alternative convenient approach to linear regression. In this paper, we develop a novel bootstrap technique based on perturbation resampling method for approximating the distribution of the maximum likelihood estimator (MLE) of the regression parameter vector. We establish second order correctness of the proposed bootstrap method after proper studentization and smoothing. It is shown that inferences drawn based on the proposed bootstrap method are more accurate compared to that based on asymptotic normality. The main challenge in establishing second order correctness remains in the fact that the response variable being binary, the resulting MLE has a lattice structure. We show the direct bootstrapping approach fails even after studentization. We adopt smoothing technique developed in Lahiri (1993) to ensure that the smoothed studentized version of the MLE has a density. Similar smoothing strategy is employed to the bootstrap version also to achieve second order correct approximation.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2007.01615
- https://arxiv.org/pdf/2007.01615
- OA Status
- green
- References
- 27
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W3038443630
All OpenAlex metadata
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- OpenAlex ID
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https://openalex.org/W3038443630Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2007.01615Digital Object Identifier
- Title
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On Second order correctness of Bootstrap in Logistic RegressionWork title
- Type
-
preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
-
2020Year of publication
- Publication date
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2020-07-03Full publication date if available
- Authors
-
Debraj Das, Priyam DasList of authors in order
- Landing page
-
https://arxiv.org/abs/2007.01615Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2007.01615Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2007.01615Direct OA link when available
- Concepts
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Correctness, Smoothing, Mathematics, Resampling, Estimator, Logistic regression, Studentized range, Asymptotic distribution, Bootstrapping (finance), Statistics, Bootstrap aggregating, Applied mathematics, Econometrics, Computer science, Algorithm, Standard errorTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- References (count)
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27Number of works referenced by this work
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.banking, | 9 |
| abstract_inverted_index.clinical | 4 |
| abstract_inverted_index.compared | 86 |
| abstract_inverted_index.density. | 148 |
| abstract_inverted_index.employed | 153 |
| abstract_inverted_index.logistic | 15 |
| abstract_inverted_index.proposed | 63, 80 |
| abstract_inverted_index.response | 12, 107 |
| abstract_inverted_index.smoothed | 140 |
| abstract_inverted_index.strategy | 151 |
| abstract_inverted_index.surveys, | 7 |
| abstract_inverted_index.variable | 108 |
| abstract_inverted_index.bootstrap | 34, 64, 81, 156 |
| abstract_inverted_index.challenge | 95 |
| abstract_inverted_index.developed | 132 |
| abstract_inverted_index.establish | 57 |
| abstract_inverted_index.estimator | 49 |
| abstract_inverted_index.parameter | 54 |
| abstract_inverted_index.resulting | 112 |
| abstract_inverted_index.smoothing | 130, 150 |
| abstract_inverted_index.technique | 35, 131 |
| abstract_inverted_index.variable, | 13 |
| abstract_inverted_index.asymptotic | 91 |
| abstract_inverted_index.biomedical | 6 |
| abstract_inverted_index.considered | 18 |
| abstract_inverted_index.convenient | 22 |
| abstract_inverted_index.inferences | 75 |
| abstract_inverted_index.likelihood | 48 |
| abstract_inverted_index.marketing, | 8 |
| abstract_inverted_index.normality. | 92 |
| abstract_inverted_index.regression | 16, 53 |
| abstract_inverted_index.resampling | 39 |
| abstract_inverted_index.smoothing. | 70 |
| abstract_inverted_index.structure. | 117 |
| abstract_inverted_index.alternative | 21 |
| abstract_inverted_index.correctness | 60, 100 |
| abstract_inverted_index.dichotomous | 11 |
| abstract_inverted_index.regression. | 26 |
| abstract_inverted_index.studentized | 141 |
| abstract_inverted_index.distribution | 44 |
| abstract_inverted_index.establishing | 97 |
| abstract_inverted_index.perturbation | 38 |
| abstract_inverted_index.approximating | 42 |
| abstract_inverted_index.bootstrapping | 122 |
| abstract_inverted_index.approximation. | 164 |
| abstract_inverted_index.studentization | 68 |
| abstract_inverted_index.studentization. | 127 |
| cited_by_percentile_year | |
| countries_distinct_count | 2 |
| institutions_distinct_count | 2 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/8 |
| sustainable_development_goals[0].score | 0.46000000834465027 |
| sustainable_development_goals[0].display_name | Decent work and economic growth |
| citation_normalized_percentile |