Non-asymptotic approximations for Pearson's chi-square statistic and its application to confidence intervals for strictly convex functions of the probability weights of discrete distributions Article Swipe
Eric Bax
,
Frédéric Ouimet
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2309.01882
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2309.01882
In this paper, we develop a non-asymptotic local normal approximation for multinomial probabilities. First, we use it to find non-asymptotic total variation bounds between the measures induced by uniformly jittered multinomials and the multivariate normals with the same means and covariances. From the total variation bounds, we also derive a comparison of the cumulative distribution functions and quantile coupling inequalities between Pearson's chi-square statistic (written as the normalized quadratic form of a multinomial vector) and its multivariate normal analogue. We apply our results to find confidence intervals for the negative entropy of discrete distributions. Our method can be applied more generally to find confidence intervals for strictly convex functions of the weights of discrete distributions.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2309.01882
- https://arxiv.org/pdf/2309.01882
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4386557295
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- OpenAlex ID
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https://openalex.org/W4386557295Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2309.01882Digital Object Identifier
- Title
-
Non-asymptotic approximations for Pearson's chi-square statistic and its application to confidence intervals for strictly convex functions of the probability weights of discrete distributionsWork title
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2023Year of publication
- Publication date
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2023-09-05Full publication date if available
- Authors
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Eric Bax, Frédéric OuimetList of authors in order
- Landing page
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https://arxiv.org/abs/2309.01882Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2309.01882Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2309.01882Direct OA link when available
- Concepts
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Mathematics, Multinomial distribution, Quantile, Statistics, Multivariate statistics, Confidence interval, Statistic, Multivariate normal distribution, CDF-based nonparametric confidence interval, Applied mathematicsTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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