Improved small-sample inference for functions of parameters in the k-sample multinomial problem Article Swipe
Michael C. Sachs
,
Erin E. Gabriel
,
Michael P. Fay
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2406.19141
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2406.19141
When the target parameter for inference is a real-valued, continuous function of probabilities in the $k$-sample multinomial problem, variance estimation may be challenging. In small samples or when the function is nondifferentiable at the true parameter, methods like the nonparametric bootstrap or delta method may perform poorly. We develop an exact inference method that applies to this general situation. We prove that our proposed exact p-value correctly bounds the type I error rate and the associated confidence intervals provide at least nominal coverage; however, they are generally difficult to implement. Thus, we propose a Monte Carlo implementation to estimate the exact p-value and confidence intervals that we show to be consistent as the number of iterations grows. Our approach is general in that it applies to any real-valued continuous function of multinomial probabilities from an arbitrary number of samples and with different numbers of categories.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2406.19141
- https://arxiv.org/pdf/2406.19141
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4400163220
All OpenAlex metadata
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- OpenAlex ID
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https://openalex.org/W4400163220Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2406.19141Digital Object Identifier
- Title
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Improved small-sample inference for functions of parameters in the k-sample multinomial problemWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2024Year of publication
- Publication date
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2024-06-27Full publication date if available
- Authors
-
Michael C. Sachs, Erin E. Gabriel, Michael P. FayList of authors in order
- Landing page
-
https://arxiv.org/abs/2406.19141Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2406.19141Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2406.19141Direct OA link when available
- Concepts
-
Multinomial distribution, Confidence interval, Sample (material), Statistics, Mathematics, Robust confidence intervals, Econometrics, Applied mathematics, Physics, ThermodynamicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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