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A Journal of Theoretical and Applied Statistics
Volume 52, 2018 - Issue 6
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Original Articles

Empirical likelihood test for equality of two distributions using distance of characteristic functions

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Pages 1379-1394 | Received 22 Aug 2017, Accepted 03 Sep 2018, Published online: 14 Sep 2018

References

  • Kolmogorov AN. Sulla determinazione empirica di una legge di distribuzione. G delllstituto Ital degli Attuari. 1933;4:83–91.
  • Smirnov N. Table for estimating the goodness of fit of empirical distributions. Ann Math Stat. 1948;19:279–281.
  • Cramér H. On the composition of elementary errors. Scand Actuar J. 1928;1:13–74.
  • Von Mises RE. Wahrscheinlichkeit, statistik und wahrheit. Berlin: Julius Springer; 1928.
  • Meintanis SG. A Kolmogorov–Smirnov type test for Skew Normal distributions based on the empirical moment generating function. J Stat Plan Inference. 2007;137:2681–2688.
  • Mood AM. The distribution theory of runs. Ann Math Stat. 1940;11:367–392.
  • Justel A, Peña D, Zamar R. A multivariate Kolmogorov–Smirnov test of goodness of fit. Stat & Probab Lett. 1997;35:251–259.
  • Friedman JH, Rafsky LC. Multivariate generalizations of the Wald-Wolfowitz and Smirnov two-sample tests. Ann Stat. 1979;7:697–717.
  • Meintanis SG. Permutation tests for homogeneity based on the empirical characteristic function. J Nonparametr Stat. 2005;17:583–592.
  • Alba Fernández V, Jiménez Gamero M.D, Muñoz García J. A test for the two-sample problem based on empirical characteristic functions. Comput Stat & Data Anal. 2008;52:3730–3748.
  • Liu ZY, Modarres R. A triangle test for equality of distribution functions in high dimensions. J Nonparametr Stat. 2011;23:605–615.
  • Biswas M, Ghosh AK. A nonparametric two-sample test applicable to high dimensional data. J Multivar Anal. 2014;123:160–171.
  • Bera AK, Ghosh A, Xiao Z. A smooth test for the equality of distributions. Econ Theory. 2013;29:419–446.
  • Zhou WX, Zheng C, Zhang Z. Two-sample smooth tests for the equality of distributions. Bernoulli. 2017;23:951–989.
  • Neyman J. Smooth test for goodness of fit. Scand Actuar J. 1937;1937:149–199.
  • Meintanis SG. A review of testing procedures based on the empirical characteristic function. S Afr Stat J. 2016;50:1–14.
  • Owen AB. Empirical likelihood ratio confidence intervals for a single functional. Biometrika. 1988;75:237–249.
  • Owen AB. Empirical likelihood ratio confidence regions. Ann Stat. 1990;18(1):90–120.
  • Owen AB. Empirical likelihood. London: Chapman & Hall; 2001.
  • Chen S, Van Keilegom I. A review on empirical likelihood methods for regression (with discussion). Test. 2009;18:415–447.
  • Székely GJ, Rizzo ML. Testing for equal distributions in high dimension. InterStat. Nov 2004;5:1249–1272.
  • Wood ATA, Do K -A, Broom BM. Sequential linearization of empirical likelihood constraints with application to u-statistics. J Comput Graph Stat. 1996;5:365–385.
  • Jing BY, Yuan JQ, Zhou W. Empirical likelihood for non-degenerate U-statistics. Stat & Probab Lett. 2008;78:599–607.
  • Arvesen JN. Jackknife U-statistics. Ann Math Stat. 1969;40:2076–2100.
  • Chen YJ, Ning W., Gupta Arjun K.. Jackknife empirical likelihood method for testing the equality of two variances. J Appl Stat. 2015;42:144–160.
  • Gong Y, Peng L, Qi YC. Smoothed jackknife empirical likelihood method for ROC curve. J Multivar Anal. 2010;101:1520–1531.
  • Li Z, Xu J, Zhou W. On nonsmooth estimating functions via jackknife empirical likelihood. Scand J Stat. 2016;43:49–69.
  • Lin HL, Li ZP, Wang DL, et al. Jackknife empirical likelihood for the error variance in linear models. J Nonparametr Stat. 2017;29(2):151–166.
  • Peng L. Approximate jackknife empirical likelihood method for estimating equations. Can J Stat. 2012;40:110–123.
  • Peng L, Qi Y. Smoothed jackknife empirical likelihood method for tail copulas. Test. 2010;19:514–536.
  • Liu X, Wang Q, Liu Y. A consistent jackknife empirical likelihood test for distribution functions. Ann Inst Stat Math. 2017;69(2):249–269.
  • Liu Y, Liu Z, Zhou W. A test for equality of two distributions via integrating characteristic functions. Stat Sin. 2018;92:97–114. To appear.
  • Baringhaus L, Franz C. On a new multivariate two-sample test. J Multivar Anal. 2004;88:190–206.
  • Jing BY. Two-sample empirical likelihood method. Stat & Probab Lett. 1995;24:315–319.
  • Hoeffding W. A class of statistics with asymptotically normal distribution. Ann Math Stat. 1948;19:293–325.
  • Huskova M, Meintanis S. Testing procedures based on the empirical characteristic function II: k-sample problem, change point problem. Tatr Mt Math Publ (Slovak Acad Sci Math Inst). 2008;39:235–243.
  • Huskova M, Meintanis S. Tests for the multivariate k-sample problem based on the empirical characteristic function. J Nonparametr Stat. 2008;20:263–277.
  • Jing BY, Yuan JQ, Zhou W. Jackknife empirical likelihood. J Am Stat Assoc. 2009;104:1224–1232.
  • Claeskens G, Jing B, Peng L, et al. Empirical likelihood confidence regions for comparison distributions and ROC curves. Can J Stat. 2003;31:173–190.

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