Acta mathematica scientia, Series B >
MAXIMIN EFFICIENCY ROBUST TEST FOR MULTIPLE NUISANCE PARAMETERS AND ITS STATISTICAL PROPERTIES
Received date: 2015-09-07
Revised date: 2016-04-29
Online published: 2017-02-25
Supported by
This work is partially supported by the Natural Science Foundation of China (11401240, 11471135), and the self-determined research funds of CCNU from the colleges' basic research of MOE (CCNU15A05038, CCNU15ZD011).
We propose the maximin efficiency robust test (MERT) for multiple nuisance parameters based on theories about the maximin efficiency robust test for only one nuisance parameter and investigate some theoretical properties about this robust test. We explore some theoretical properties about the power of the MERT for multiple nuisance parameters in a specified scenario intuitively further more. We also propose a meaningful example from statistical genetic field to which the MERT for multiple nuisance parameters can be well applied. Extensive simulation studies are conducted to testify the robustness of the MERT for multiple nuisance parameters.
Qing YANG , Jiayan ZHU , Zhengbang LI . MAXIMIN EFFICIENCY ROBUST TEST FOR MULTIPLE NUISANCE PARAMETERS AND ITS STATISTICAL PROPERTIES[J]. Acta mathematica scientia, Series B, 2017 , 37(1) : 223 -234 . DOI: 10.1016/S0252-9602(16)30127-8
[1] Serfling R J. Approximation Theorems of Mathematical Statistics. New York:John Wiley & Sons, 1980
[2] Noether G E. On a theorem of Pitman. Ann Math Statist, 1955, 26:64-68
[3] Gastwirth J L. On robust procedures. J Amer Stat Ass, 1966, 61:929-948
[4] Gastwirth J L. The use of maximin efficiency robust tests in combining contingency tables and survival analysis. J Amer Stat Ass, 1985, 80:380-384
[5] Zheng G, Li Q Z, Yuan A. Some statistical properties of efficiency robust test with applications to genetic association studies. Scand J Stat Theory Appl, 2014, 41:762-774
[6] Birnbaum A, Laska E. Efficiency robust 2-sample rank test. J Amer Stat Ass, 1967, 62:1241-1251
[7] Barndorff-Nielsen O E, Cox D R. Inference and Asymptotics. Florida:Chapman and Hall/CRC Press, 1994
[8] Gastwirth J L, Freidlin B. On power and efficiency robust linkage tests for affected sibs. Ann Hum Genet, 2000, 64:443-453
[9] Freidlin B, Zheng G, Li Z, Gastwirth J L. Trend tests for case-ontrol studies of genetic markers:power, sample size and robustness. Hum Hered, 2002, 53:146-152
[10] So H-C, Sham P C. Robust association tests under differrent genetic models, allowing for binary or quantitative trait and covariate. Behav Genet, 2011, 41:768-775
[11] Schaid D J, Sommer S S. Genotype relative risks-methods for design and analysis of candidate-gene association studies. Am J Hum Genet, 1993, 53:1114-1126
[12] Sasieni P D. From genotypes to genes:doubling the sample size. Biometrics, 1997, 53:1253-1261
[13] CochranWG. Some methods for strengthening the common chi-square tests. Biometrics, 1954, 10:417-451
[14] Armitage P. Tests for linear trends in proportions and frequencies. Biometrics, 1955, 11:375-386
[15] Zheng G, Joo J, Yang Y. Pearson's test, trend test and MAX are all trends tests with different types of scores. Ann Hum Genet, 2009, 73:133-140
[16] Xiong M, Zhao J, Boerwinkle E. Generalized T2 test for genome association studies. Am J Hum Genet, 2002, 70:1257-1268
[17] Chapman J M, Cooper J D, Todd J A, Clayton D G. Detecting disease associations due to linkage disequi-ibrium using haplotype tags:a class of tests and the determinants of statistical power. Hum Hered, 2003, 56:18-31
[18] Fan R, Knapp M. Genome association studies of complex diseases by case-control designs. Am J Hum Genet, 2003, 72:850-868
[19] Li Q Z, Zheng G, Li Z H, Yu K. Efficient Approximation of P-value of the Maximum of Correlated Tests, with Applications to Genome-Wide Association Studies. Ann Human Genetics, 2008, 72:397-406
[20] Chatterjee N, Chen Y-H, Luo S, Carroll R J. Analysis of Case-Control Association Studies:SNPs, Imputation and Haplotypes. Stat Sci, 2009, 24:489-502
[21] Ballard D H, Cho J, Zhao, H Y. Comparisons of multi-marker association methods to detect association between a candidate region and disease. Genetic Epidemiology, 2010, 34:201-212
/
| 〈 |
|
〉 |