Journal article
The Pearson Score Statistic for Multinomial-Poisson Models
Communications in Statistics - Theory and Methods, Vol.43(21), pp.4471-4491
11/02/2014
DOI: 10.1080/03610926.2012.714036
Abstract
The score statistic S 2 is commonly used for general likelihood-based inference. Pearson's Chi-squared statistic X 2 = ∑(O − E) 2 /E is ubiquitous in contingency table inference. Because tests and confidence intervals based on S 2 have been shown to work well in practice and theory and because X 2 has such a simple and intuitively appealing form, it is of interest to know when S 2 is identical to X 2 and when X 2 has an approximate Chi-squared distribution. Toward these ends, this paper gives a simple proof that S 2 = X 2 for the broad class of multinomial-Poisson distributions when the alternative hypothesis is unrestricted in a certain sense. This paper also gives a sufficient condition under which the null distribution of the Pearson score statistic is approximately Chi-squared. Several examples illustrate the utility of the results and counter-examples highlight the importance of the sufficient conditions of the results.
Details
- Title: Subtitle
- The Pearson Score Statistic for Multinomial-Poisson Models
- Creators
- Joseph B Lang - Department of Statistics and Actuarial Science, University of Iowa
- Resource Type
- Journal article
- Publication Details
- Communications in Statistics - Theory and Methods, Vol.43(21), pp.4471-4491
- Publisher
- Taylor & Francis
- DOI
- 10.1080/03610926.2012.714036
- ISSN
- 0361-0926
- eISSN
- 1532-415X
- Language
- English
- Date published
- 11/02/2014
- Academic Unit
- Statistics and Actuarial Science; Biostatistics
- Record Identifier
- 9983985810802771
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