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Article

Keywords:
dimensional asymptotics; genomics; multiple hypotheses testing; microarray data model; nonparametrics; U-statistics
Summary:
High-dimensional data models abound in genomics studies, where often inadequately small sample sizes create impasses for incorporation of standard statistical tools. Conventional assumptions of linearity of regression, homoscedasticity and (multi-) normality of errors may not be tenable in many such interdisciplinary setups. In this study, Kendall's tau-type rank statistics are employed for statistical inference, avoiding most of parametric assumptions to a greater extent. The proposed procedures are compared with Kendall's tau statistic based ones. Applications in microarray data models are stressed.
References:
[1] Arratia, R., Goldstein, L., Gordon, L.: Two moments suffice for Poisson approximations: The Chen-Stein method. Ann. Probab. 17 (1989), 9-25. DOI 10.1214/aop/1176991491 | MR 0972770 | Zbl 0675.60017
[2] Arratia, R., Goldstein, L., Gordon, L.: Poisson approximation and the Chen-Stein method. Stat. Sci. 5 (1990), 403-424. MR 1092983 | Zbl 0955.62542
[3] Arratia, R., Goldstein, L., Gordon, L.: Poisson approximation and the Chen-Stein method: Rejoinder. Stat. Sci. 5 (1990), 432-434. MR 1092983
[4] Benjamini, Y., Hochberg, Y.: Controlling the false discovery rate: A practical and powerful approach to multiple testing. J. R. Stat. Soc., Ser. B 57 (1995), 289-300. MR 1325392 | Zbl 0809.62014
[5] Chen, L. H. Y.: Poisson approximation for dependent trials. Ann. Probab. 3 (1975), 534-545. DOI 10.1214/aop/1176996359 | MR 0428387 | Zbl 0335.60016
[6] Chen, L. H. Y.: Poisson approximation and the Chen-Stein method: Comment. Stat. Sci. 5 (1990), 429-432. MR 1092983
[7] Goldstein, L., Watterman, M.: Poisson, compound Poisson and process approximations for testing statistical significance in sequence comparisons. Bull. Math. Biol. 54 (1992), 785-812. DOI 10.1007/BF02459930
[8] Goldstein, L., Xia, A.: Zero biasing and a discrete central limit theorem. Ann. Probab. 34 (2006), 1782-1806. DOI 10.1214/009117906000000250 | MR 2271482 | Zbl 1111.60015
[9] Jurečková, J., Sen, P. K.: Robust Statistical Procedures: Asymptotics and Interrelations. Wiley Series. Wiley & Sons New York (1996). MR 1387346
[10] Kang, M.: Multiple testing in genome-wide studies. UNC Biostatistics Thesis (2007).
[11] Kendall, M. G.: A new measure of rank correlation. Biometrika 30 (1938), 81-93. DOI 10.1093/biomet/30.1-2.81 | Zbl 0019.13001
[12] Lobenhofer, E. K., Bennett, L., Cable, P. L., Li, L., Bushel, P. R., Afshari, C. A.: Regulation of DNA replication fork genes by 17-estradiol. Molecular Endocrinology 16 (2002), 1215-1229.
[13] Roy, S. N.: On a heuristic method of test construction and its use in multivariate analysis. J. Ann. Math. Stat. 24 (1953), 220-238. DOI 10.1214/aoms/1177729029 | MR 0057519 | Zbl 0051.36701
[14] Sarkar, S. K., Chang, C.-K.: The Simes method for multiple hypothesis testing with positively dependent test statistics. J. Am. Stat. Assoc. 92 (1997), 1601-1608. DOI 10.1080/01621459.1997.10473682 | MR 1615269 | Zbl 0912.62079
[15] Sen, P. K.: Estimates of the regression coefficients based on Kendall's tau. J. Am. Stat. Assoc. 63 (1968), 1379-1389. DOI 10.1080/01621459.1968.10480934 | MR 0258201
[16] Sen, P. K.: Robust statistical inference for high-dimensional data models with application to genomics. Aust. J. Stat. 35 (2006), 197-211.
[17] Sen, P. K.: Kendall's tau in high-dimension genomics parsimony. IMS Collection 3 (2008), 250-265. MR 2459229
[18] Sen, P. K., Tsai, M.-T., Jou, Y.-S.: High-dimension low sample size perspectives in constrained statistical inference: The SARSCoV RNA genome in illustration. J. Am. Stat. Assoc. 102 (2007), 686-694. DOI 10.1198/016214507000000077 | MR 2370860 | Zbl 1172.62335
[19] Storey, J.: A direct approach to false discovery rates. J. R. Stat. Soc., Ser. B 64 (2002), 479-498. DOI 10.1111/1467-9868.00346 | MR 1924302 | Zbl 1090.62073
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