Improving Tests for Discrete Small Sample Data
Springer Verlag, Singapore
978-981-95-5300-6 (ISBN)
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Mainly, for the phi-divergence family of statistics that include Pearson’s chi-square statistic, the log-likelihood ratio statistic, and the power divergence family of statistics as a special case, the book derives the improvement of statistics as transformed statistics. This accomplishment is achieved by using the expression of approximation of the distribution of original phi-divergence statistics based on Edgeworth expansion. For an independence model of a contingency table, a complete independence model, an independence model among a group of factors, and a conditional independence model are considered. The test statistics of a contingency table for a log-linear model are also presented for consideration. Additionally, the selection of statistics for which the distribution is close to the limiting distribution is discussed using the evaluation of second-order correction of moments.
Nobuhiro Taneichi received his master degree from Hokkaido University in 1984 and the degree of Doctor of Philosophy in Engineering from Hokkaido University in 1995. His working career started as Assistant Professor at Obihiro University of Agriculture and Veterinary Medicine, 1988, Associate Professor at Obihiro University of Agriculture and Veterinary Medicine, 1996, Professor at Obihiro University of Agriculture, 2001, Professor at Department of Mathematics and Computer Science in Kagoshima University, 2006, Professor at Hokkaido University of Education, Sapporo Campus, 2017-2023. His research interest is primarily statistics, including categorical data analysis (generalized linear model, independence models of contingency table, loglinear models of contingency table), statistical inference based on divergence and asymptotic expansion for probability of discrete multivariate statistics. He has published works in several academic journals, including Journal of Multivariate Analysis, Annals of the Institute of Statistical Mathematics, Japanese Journal of Statistics and Data Science, Journal of Statistical Planning and Inference and Journal of the Japan Statistical Society. Yuri Sekiya received her master degree from Hokkaido University in 1988 and the degree of Doctor of Philosophy in Engineering from Hokkaido University in 2004. Her working career started as Assistant at Hokkaido University of Education, 1989, Lecturer at Hokkaido University of Education, 1991, Assistant Professor at Hokkaido University of Education, 1994, Professor at Hokkaido University of Education, Kushiro Campus, 2005-2025. Her research interest is primarily statistics, including categorical data analysis (generalized linear model, independence models of contingency table, loglinear models of contingency table), statistical inference based on divergence and asymptotic expansion for probability of discrete multivariate statistics. She has published works in several academic journals, including Journal of Multivariate Analysis and Journal of the Japan Statistical Society.
Chapter 1.Purpose of this book.- Chapter 2.Preliminary results.- Chapter 3. Transformed statistic for the test of independence in J x K contingency table.- Chapter 4. A transformed statistic for the test of complete independence in a contingency table.- Chapter 5. A transformed statistic for the test of conditional independence in a J x K x L table.- Chapter 6. A transformed goodness-of-fit statistic for a generalized linear model of binary data.- Chapter 7. A transformed goodness-of-fit statistic for a loglinear model in a contingency table.- Chapter 8. The selection of statistics based on a second-order correction term when data are not so large.- Chapter 9. Constructing a new statistic NT for testing complete independence in contingency tables.- Chapter 10. Summary and Conclusion.
| Erscheint lt. Verlag | 21.2.2026 |
|---|---|
| Reihe/Serie | JSS Research Series in Statistics | SpringerBriefs in Statistics |
| Zusatzinfo | 1 Illustrations, black and white |
| Verlagsort | Singapore |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik |
| Schlagworte | asymptotic expansion • Contingency table • discrete data • GLIM • Improved Transformation • Independence • Log-linear Model • Phi-Divergence Statistics • Small Sample • sparse data |
| ISBN-10 | 981-95-5300-8 / 9819553008 |
| ISBN-13 | 978-981-95-5300-6 / 9789819553006 |
| Zustand | Neuware |
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