×

zbMATH — the first resource for mathematics

New non-parametric tests for independence. (English) Zbl 07194340
Summary: In this paper, we consider the problem of testing independence against stochastically increasing property. For the construction of new statistical tests, we employ Nadaraya-Watson regression estimator. We examine their asymptotic properties under the null and an alternative hypothesis. The performance of the tests is studied via power study. For this purpose, the bootstrap versions of proposed tests are utilized. The finite sample results indicate their competitiveness compared to existing statistical methods.
MSC:
60E15 Inequalities; stochastic orderings
60K10 Applications of renewal theory (reliability, demand theory, etc.)
Software:
copula; testforDEP
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Block HW, Ting ML.Some concepts of multivariate dependence. Comm Statist Theory Methods. 1981;10:749-762. doi: 10.1080/03610928108828072[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 0478.62045
[2] Esary JD, Proschan F.Relationships among some notions of bivariate dependence. Ann Math Statist. 1972;43:651-655. doi: 10.1214/aoms/1177692646[Crossref], [Google Scholar] · Zbl 0263.62011
[3] Lehmann EL.Some concepts of dependence. Ann Math Statist. 1966;37:1137-1153. doi: 10.1214/aoms/1177699260[Crossref], [Google Scholar] · Zbl 0146.40601
[4] Harris R.A multivariate definition of increasing hazard rate distribution functions. Ann Math Statist. 1970;41:713-717. doi: 10.1214/aoms/1177697121[Crossref], [Google Scholar] · Zbl 0196.22005
[5] Kochar SC, Gupta RP.Competitors of the Kendall’s tan test for testing independence against positive quadrant dependence. Biometrika. 1987;74:664-666. doi: 10.1093/biomet/74.3.664[Crossref], [Web of Science ®], [Google Scholar] · Zbl 0628.62049
[6] Kochar SC, Gupta RP.Distribution-free tests based on sub-sample extrema for testing against positive quadrant dependence. Aust J Statist. 1990;32:45-51. doi: 10.1111/j.1467-842X.1990.tb00998.x[Crossref], [Google Scholar] · Zbl 0707.62083
[7] Güven B, Kotz S.Test of independence for generalized Farlie-Gumbel-Morgenstern distributions. J Comput Appl Math. 2008;212(1):102-111. doi: 10.1016/j.cam.2006.11.029[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1130.62021
[8] Shetty ID, Pandit PV.A class of distribution-free tests for testing independence against positive quadrant dependence. Assam Stat Rev. 1998;12:42-50. [Google Scholar]
[9] Shetty ID, Pandit PV.A distribution-free test for positive quadrant dependence. J Indian Soc Probab Statist. 1996;3-4:41-52. [Google Scholar]
[10] Shetty ID, Pandit PV.Distribution-free tests for independence against positive quadrant dependence: a generalization. Stat Methods Appl. 2003;12(1):5-17. doi: 10.1007/BF02511580[Crossref], [Google Scholar] · Zbl 1056.62058
[11] Zargar M, Jabbari Nooghabi H, Amini M.Test of independence for Baker’s bivariate distributions. Comm Statist Simulation Comput. 2016;45(9):3074-3093. doi: 10.1080/03610918.2014.917676[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1348.62181
[12] Zargar M, Jabbari H, Amini M.Dependence structure and test of independence for some well-known bivariate distribution. Comput Stat. 2017;32(4):1423-1451. doi: 10.1007/s00180-016-0696-9[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1417.62132
[13] Aly EEA, Kochar SC.On testing for independence against right tail increasing in bivariate models. Metrika. 1994;41(1):211-225. doi: 10.1007/BF01895319[Crossref], [Google Scholar] · Zbl 0802.62050
[14] Nadaraya EA.On estimating regression. Theory Probab Appl. 1964;9:141-142. doi: 10.1137/1109020[Crossref], [Google Scholar]
[15] Watson G.Smooth regression analysis. Sankhya. 1964;26:359-372. [Google Scholar] · Zbl 0137.13002
[16] Cai Z.Regression quantiles for time series. Econ Theory. 2002;18:169-192. doi: 10.1017/S0266466602181096[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1181.62124
[17] Li Q, Racine J. Nonparametric econometrics: theory and practice. Princeton University Press; 2007. [Google Scholar] · Zbl 1183.62200
[18] Hall P, Wolff C, Yao Q.Methods for estimating a conditional distribution function. J Am Stat Assoc. 1999;94:154-163. doi: 10.1080/01621459.1999.10473832[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1072.62558
[19] Simonoff J. Smoothing methods in statistics. New York: Springer; 1996. [Crossref], [Google Scholar] · Zbl 0859.62035
[20] Silverman BW. Density estimation for statistics and data analysis. London: Chapman and Hall; 1986. [Crossref], [Google Scholar]
[21] Genest C, Rémillard B.Test of independence and randomness based on the empirical copula process. Test. 2004;13(2):335-369. doi: 10.1007/BF02595777[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1069.62039
[22] Miecznikowski JC, Hsu ES, Chen Y, et al. testforDEP: an R package for distribution-free tests and visualization tools for independence. 2017. (SUNY university at buffalo biostatistics technical reports; 1701, 2). [Google Scholar]
[23] Hofert M, Kojadinović I, Maechler M, et al. copula: multivariate dependence with copulas. R package version 0.999-19.1; 2018. Available from: https://CRAN.R-project.org/package=copula. [Google Scholar]
[24] Balakrishnan N, Lai CD. Continuous bivariate distributions. New York: Springer Science & Business Media; 2009. [Google Scholar] · Zbl 1267.62028
[25] Miklós C, Lajos H.A note on strong approximations of multivariate empirical processes. Stoch Process Appl. 1988;28:101-109. doi: 10.1016/0304-4149(88)90068-3[Crossref], [Web of Science ®], [Google Scholar] · Zbl 0651.60040
[26] Block HW, Basu AP.A continuous bivariate exponential extension. J Am Stat Assoc. 1974;69:1031-1037. [Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 0299.62027
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.