TY - JOUR
T1 - An efficient nonparametric test for bivariate two-sample location problem
AU - Mathur, Sunil K.
AU - Smith, Pamela F.
PY - 2008/3
Y1 - 2008/3
N2 - We propose a new test for the two-sample bivariate location problem. The proposed test statistic has a U-statistic representation with a degenerate kernel. The limiting distribution is found for the proposed test statistic. The power of the test is compared using Monte Carlo simulation to the tests of Blumen [I. Blumen, A new bivariate sign-test for location, Journal of the American Statistical Association 53 (1958) 448-456], Mardia [K.V. Mardia, A non-parametric test for the bivariate two-sample location problem, Journal of the Royal Statistical Society, Series B 29 (1967) 320-342], Peters and Randles [D. Peters, R.H. Randles, A bivariate signed-rank test for the two-sample location problem, Journal of the Royal Statistical Society, Series B 53 (1991) 493-504], LaRocque, Tardif and van Eeden [D. LaRocque, S. Tardif, C. van Eeden, An affine-invariant generalization of the Wilcoxon signed-rank test for the bivariate location problem, Australian and New Zealand Journal of Statistics 45 (2003) 153-165], and Baringhaus and Franz [L. Baringhaus, C. Franz, On a new multivariate two-sample test, Journal of Multivariate Analysis 88 (2004) 190-206]. Under the bivariate normal and bivariate t distributions the proposed test was more powerful than the competitors for almost every change in location. Under the other distributions the proposed test reached the desired power of one at a faster rate than the other tests in the simulation study. Application of the test is presented using bivariate data from a synthetic and a real-life data set.
AB - We propose a new test for the two-sample bivariate location problem. The proposed test statistic has a U-statistic representation with a degenerate kernel. The limiting distribution is found for the proposed test statistic. The power of the test is compared using Monte Carlo simulation to the tests of Blumen [I. Blumen, A new bivariate sign-test for location, Journal of the American Statistical Association 53 (1958) 448-456], Mardia [K.V. Mardia, A non-parametric test for the bivariate two-sample location problem, Journal of the Royal Statistical Society, Series B 29 (1967) 320-342], Peters and Randles [D. Peters, R.H. Randles, A bivariate signed-rank test for the two-sample location problem, Journal of the Royal Statistical Society, Series B 53 (1991) 493-504], LaRocque, Tardif and van Eeden [D. LaRocque, S. Tardif, C. van Eeden, An affine-invariant generalization of the Wilcoxon signed-rank test for the bivariate location problem, Australian and New Zealand Journal of Statistics 45 (2003) 153-165], and Baringhaus and Franz [L. Baringhaus, C. Franz, On a new multivariate two-sample test, Journal of Multivariate Analysis 88 (2004) 190-206]. Under the bivariate normal and bivariate t distributions the proposed test was more powerful than the competitors for almost every change in location. Under the other distributions the proposed test reached the desired power of one at a faster rate than the other tests in the simulation study. Application of the test is presented using bivariate data from a synthetic and a real-life data set.
KW - Bivariate
KW - Location
KW - Power
KW - Test
KW - Two-sample
UR - http://www.scopus.com/inward/record.url?scp=39049096162&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=39049096162&partnerID=8YFLogxK
U2 - 10.1016/j.stamet.2007.07.001
DO - 10.1016/j.stamet.2007.07.001
M3 - Article
AN - SCOPUS:39049096162
SN - 1572-3127
VL - 5
SP - 142
EP - 159
JO - Statistical Methodology
JF - Statistical Methodology
IS - 2
ER -