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| Title: | Nonparametric Criteria for Sparse Contingency Tables |
| Other Titles: | Neparametriniai kriterijai retų įvykių dažnių lentelėms |
| Authors: | Samusenko, Pavel |
| Issue Date: | 2012 |
| Publisher: | VGTU leidykla „TECHNIKA“ |
| Citation: | Samusenko, P. 2012. Nonparametric Criteria for Sparse Contingency Tables: doctoral dissertation. Vilnius: Technika. 116 p. |
| Description: | In the dissertation, the problem of nonparametric testing for sparse contin- gency tables is addressed.
Statistical inference problems caused by sparsity of contingency tables are widely discussed in the literature. Traditionally, the expected (under null the hypothesis) frequency is required to exceed 5 in almost all cells of the contingency table. If this condition is violated, the χ2 approximations of goodness-of-fit statistics may be inaccurate and the table is said to be sparse. Several techniques have been proposed to tackle the problem: exact tests, alternative approximations, parametric and nonparametric bootstrap, Bayes approach and other methods. However they all are not applicable or have some limitations in nonparametric statistical inference of very sparse contingency tables.
In the dissertation, it is shown that, for sparse categorical data, the likelihood ratio statistic and Pearson’s χ2 statistic may become noninformative: they do not anymore measure the goodness-of-fit of null hypotheses to data. Thus, they can be inconsistent even in cases where a simple consistent test does exist.
An improvement of the classical criteria for sparse contingency tables is proposed. The improvement is achieved by grouping and smoothing of sparse categorical data by making use of a new sparse asymptotics model relying on (extended) empirical Bayes approach. Under general conditions, the con- sistency of the proposed criteria based on grouping is proved. Finite-sample behavior of the criteria is investigated via Monte Carlo simulations.
The dissertation consists of four parts including Introduction, 4 chapters, General conclusions, References and Appendices.
The introduction reveals the importance of the scientific problem, describes the purpose and tasks of the thesis, research methodology, scientific novelty, the practical significance of results The introduction ends in presenting the author’s publications on the subject of the defended dissertation, offering the material of made presentations in conferences.
In Chapter 1, an overview of the problem is presented and basic definitions are introduced. Chapter 2 demonstrates the inconsistency of classical tests in case of (very) sparse categorical data for both multinomial and Poisson sam- pling scheme. In Chapter 3, extended Bayes model is introduced. It provides a basis for smoothing and grouping of sparse (nominal) data. The consistency of criteria based on grouping is proved. Finite-sample behavior of the classical and proposed criteria is studied in Chapter 4. Details of the computer simula- tion results are given in Appendix. |
| URI: | http://dspace1.vgtu.lt/handle/1/1564 |
| ISBN: | 978-609-457-394-1 |
| Appears in Collections: | Fizinių mokslų daktaro disertacijos ir jų santraukos
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