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- W2973293168 abstract "In this paper, we propose a general framework for distribution-free nonparametric testing in multi-dimensions, based on a notion of multivariate ranks defined using the theory of measure transportation. Unlike other existing proposals in the literature, these multivariate ranks share a number of useful properties with the usual one-dimensional ranks; most importantly, these ranks are distribution-free. This crucial observation allows us to design nonparametric tests that are exactly distribution-free under the null hypothesis. We demonstrate the applicability of this approach by constructing exact distribution-free tests for two classical nonparametric problems: (i) testing for mutual independence between random vectors, and (ii) testing for the equality of multivariate distributions. In particular, we propose (multivariate) rank versions of distance covariance (Sz'ekely et al., 2007) and energy statistic (Sz'ekely and Rizzo, 2013) for testing scenarios (i) and (ii) respectively. In both these problems, we derive the asymptotic null distribution of the proposed test statistics. We further show that our tests are consistent against all fixed alternatives. Moreover, the proposed tests are tuning-free, computationally feasible and are well-defined under minimal assumptions on the underlying distributions (e.g., they do not need any moment assumptions). We also demonstrate the efficacy of these procedures via extensive simulations. In the process of analyzing the theoretical properties of our procedures, we end up proving some new results in the theory of measure transportation and in the limit theory of permutation statistics using Stein's method for exchangeable pairs, which may be of independent interest." @default.
- W2973293168 created "2019-09-26" @default.
- W2973293168 creator A5024944074 @default.
- W2973293168 creator A5033475436 @default.
- W2973293168 date "2019-09-18" @default.
- W2973293168 modified "2023-10-04" @default.
- W2973293168 title "Multivariate Rank-based Distribution-free Nonparametric Testing using Measure Transportation" @default.
- W2973293168 cites W1421469996 @default.
- W2973293168 cites W1479763159 @default.
- W2973293168 cites W1490692428 @default.
- W2973293168 cites W1531237901 @default.
- W2973293168 cites W1539357586 @default.
- W2973293168 cites W1553408595 @default.
- W2973293168 cites W1638081485 @default.
- W2973293168 cites W1843806100 @default.
- W2973293168 cites W1965817835 @default.
- W2973293168 cites W1968698987 @default.
- W2973293168 cites W1968786619 @default.
- W2973293168 cites W1969130154 @default.
- W2973293168 cites W1971138433 @default.
- W2973293168 cites W1971177003 @default.
- W2973293168 cites W1971947347 @default.
- W2973293168 cites W1972978214 @default.
- W2973293168 cites W1977593285 @default.
- W2973293168 cites W1982725927 @default.
- W2973293168 cites W1985093013 @default.
- W2973293168 cites W1985514943 @default.
- W2973293168 cites W1985881163 @default.
- W2973293168 cites W1994665973 @default.
- W2973293168 cites W2001956672 @default.
- W2973293168 cites W2002190927 @default.
- W2973293168 cites W2002870907 @default.
- W2973293168 cites W2003283154 @default.
- W2973293168 cites W2004292347 @default.
- W2973293168 cites W2005388202 @default.
- W2973293168 cites W2006113200 @default.
- W2973293168 cites W2009070933 @default.
- W2973293168 cites W2010353172 @default.
- W2973293168 cites W2011292888 @default.
- W2973293168 cites W2015120816 @default.
- W2973293168 cites W2016440615 @default.
- W2973293168 cites W2018582985 @default.
- W2973293168 cites W2019841176 @default.
- W2973293168 cites W2022233105 @default.
- W2973293168 cites W2022681869 @default.
- W2973293168 cites W2023166574 @default.
- W2973293168 cites W2023205960 @default.
- W2973293168 cites W2027390033 @default.
- W2973293168 cites W2031175904 @default.
- W2973293168 cites W2035108449 @default.
- W2973293168 cites W2037027640 @default.
- W2973293168 cites W2038351084 @default.
- W2973293168 cites W2038426360 @default.
- W2973293168 cites W2039935421 @default.
- W2973293168 cites W2040012172 @default.
- W2973293168 cites W2042132284 @default.
- W2973293168 cites W2042319042 @default.
- W2973293168 cites W2045650933 @default.
- W2973293168 cites W2051991803 @default.
- W2973293168 cites W2054011126 @default.
- W2973293168 cites W2055343087 @default.
- W2973293168 cites W2068625319 @default.
- W2973293168 cites W2070803806 @default.
- W2973293168 cites W2072825306 @default.
- W2973293168 cites W2074430041 @default.
- W2973293168 cites W2076635899 @default.
- W2973293168 cites W2077584453 @default.
- W2973293168 cites W2078483536 @default.
- W2973293168 cites W2079830916 @default.
- W2973293168 cites W2079884250 @default.
- W2973293168 cites W2082760567 @default.
- W2973293168 cites W2083252561 @default.
- W2973293168 cites W2083687778 @default.
- W2973293168 cites W2084812512 @default.
- W2973293168 cites W2089013935 @default.
- W2973293168 cites W2092968642 @default.
- W2973293168 cites W2093071433 @default.
- W2973293168 cites W2099634420 @default.
- W2973293168 cites W2103679238 @default.
- W2973293168 cites W2110176078 @default.
- W2973293168 cites W2111527197 @default.
- W2973293168 cites W2112190566 @default.
- W2973293168 cites W2112552549 @default.
- W2973293168 cites W2118216969 @default.
- W2973293168 cites W2121348175 @default.
- W2973293168 cites W2121360982 @default.
- W2973293168 cites W2127961046 @default.
- W2973293168 cites W2130315424 @default.
- W2973293168 cites W2132138475 @default.
- W2973293168 cites W2132883347 @default.
- W2973293168 cites W2135681634 @default.
- W2973293168 cites W2138309709 @default.
- W2973293168 cites W2139688603 @default.
- W2973293168 cites W2141461755 @default.
- W2973293168 cites W2145544165 @default.
- W2973293168 cites W2146096861 @default.
- W2973293168 cites W2157963336 @default.
- W2973293168 cites W2166121267 @default.
- W2973293168 cites W2167897175 @default.
- W2973293168 cites W2168187896 @default.