Testing Homogeneity in a Semiparametric Two-Sample Problem
We study a two-sample homogeneity testing problem, in which one sample comes from a population with density f(x) and the other is from a mixture population with mixture density (1−λ)f(x)+λg(x). This problem arises naturally from many statistical applications such as test for partial differential ge...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2012/537474 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832559345660854272 |
|---|---|
| author | Yukun Liu Pengfei Li Yuejiao Fu |
| author_facet | Yukun Liu Pengfei Li Yuejiao Fu |
| author_sort | Yukun Liu |
| collection | DOAJ |
| description | We study a two-sample homogeneity testing problem, in which one sample comes from a population with density f(x) and the other is from a mixture population with mixture density (1−λ)f(x)+λg(x). This problem arises naturally from many statistical applications such as test for partial differential gene expression in microarray study or genetic studies for gene mutation. Under the semiparametric assumption g(x)=f(x)eα+βx, a penalized empirical likelihood ratio test could be constructed, but its implementation is hindered by the fact that there is neither feasible algorithm for computing the test statistic nor available research results on its theoretical properties. To circumvent these difficulties, we propose an EM test based on the penalized empirical likelihood. We prove that the EM test has a simple chi-square limiting distribution, and we also demonstrate its competitive testing performances by simulations. A real-data example is used to illustrate the proposed methodology. |
| format | Article |
| id | doaj-art-567819d85a6148caa985b831c9bdd7e1 |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-567819d85a6148caa985b831c9bdd7e12025-02-03T01:30:19ZengWileyJournal of Probability and Statistics1687-952X1687-95382012-01-01201210.1155/2012/537474537474Testing Homogeneity in a Semiparametric Two-Sample ProblemYukun Liu0Pengfei Li1Yuejiao Fu2Department of Statistics and Actuarial Science, School of Finance and Statistics, East China Normal University, Shanghai 200241, ChinaDepartment of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, N2L 3G1, CanadaDepartment of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3, CanadaWe study a two-sample homogeneity testing problem, in which one sample comes from a population with density f(x) and the other is from a mixture population with mixture density (1−λ)f(x)+λg(x). This problem arises naturally from many statistical applications such as test for partial differential gene expression in microarray study or genetic studies for gene mutation. Under the semiparametric assumption g(x)=f(x)eα+βx, a penalized empirical likelihood ratio test could be constructed, but its implementation is hindered by the fact that there is neither feasible algorithm for computing the test statistic nor available research results on its theoretical properties. To circumvent these difficulties, we propose an EM test based on the penalized empirical likelihood. We prove that the EM test has a simple chi-square limiting distribution, and we also demonstrate its competitive testing performances by simulations. A real-data example is used to illustrate the proposed methodology.http://dx.doi.org/10.1155/2012/537474 |
| spellingShingle | Yukun Liu Pengfei Li Yuejiao Fu Testing Homogeneity in a Semiparametric Two-Sample Problem Journal of Probability and Statistics |
| title | Testing Homogeneity in a Semiparametric Two-Sample Problem |
| title_full | Testing Homogeneity in a Semiparametric Two-Sample Problem |
| title_fullStr | Testing Homogeneity in a Semiparametric Two-Sample Problem |
| title_full_unstemmed | Testing Homogeneity in a Semiparametric Two-Sample Problem |
| title_short | Testing Homogeneity in a Semiparametric Two-Sample Problem |
| title_sort | testing homogeneity in a semiparametric two sample problem |
| url | http://dx.doi.org/10.1155/2012/537474 |
| work_keys_str_mv | AT yukunliu testinghomogeneityinasemiparametrictwosampleproblem AT pengfeili testinghomogeneityinasemiparametrictwosampleproblem AT yuejiaofu testinghomogeneityinasemiparametrictwosampleproblem |