Rank Tests for Independence and Randomness
نویسنده
چکیده
This chapter concerns rank tests for independence of two random variables. A form of locally most powerful test against particular alternative is derived and the most often used variants of this test are mentioned, namely the test of van der Waerden type, Spearman rank correlation coefficient, the quadrant test and the Kendall rank correlation coefficient, a member of non-linear rank statistics. Tests of hypothesis of randomness against trend alternatives are then studied and compared to the tests for independence that are formally similar. These tests, as well as a modification of the Kruskal-Wallis statistic in the presence of ties, are applied also to contingency tables. Modifications of all test statistics in the presence of ties and their expectation and variance formulas are given. The tests are applied and compared to each other and to classical tests of independence on examples. All of these tests are distribution free and relatively easy to use, which makes them widely applicable.
منابع مشابه
Locally Most Powerful Tests Based on Sequential Ranks
Sequential ranks of data X1, X2, . . . observed sequentially in time are defined as ranks computed from the data observed so far, denoting Rii the rank of Xi among the values X1, X2, . . . , Xi for any i. This paper studies tests of various hypotheses based on sequential ranks and derives such tests, which are locally most powerful among all tests based on sequential ranks. Such locally most po...
متن کاملModeling Multivariate Distributions with Continuous Margins Using the copula R Package
The copula-based modeling of multivariate distributions with continuous margins is presented as a succession of rank-based tests: a multivariate test of randomness followed by a test of mutual independence and a series of goodness-of-fit tests. All the tests under consideration are based on the empirical copula, which is a nonparametric rank-based estimator of the true unknown copula. The princ...
متن کاملThe Recognition and Ranking of the Dimensions of University Autonomy with Reason and Cause Approaches for the Efficiency of Islamic Azad Universities
The general purpose of this study was to identify and rank the dimensions of academic independence with causal and causal approaches in Islamic Azad universities of Mazandaran province. This research was applied in terms of purpose and descriptive in terms of method. The statistical population consisted of all faculty members of Islamic Azad universities of Mazandaran province in the number of ...
متن کاملTests of Independence and Randomness Based on the Empirical Copula Process
Deheuvels (1981a) described a decomposition of the empirical copula process into a finite number of asymptotically mutually independent sub-processes whose joint limiting distribution is tractable under the hypothesis that a multivariate distribution is equal to the product of its margins. It is proved here that this result can be extended to the serial case and that the limiting processes have...
متن کاملOn the Permutation Distribution of Independence Tests
One of the most popular class of tests for independence between two random variables is the general class of rank statistics which are invariant under permutations. This class contains Spearman’s coefficient of rank correlation statistic, Fisher-Yates statistic, weighted Mann statistic and others. Under the null hypothesis of independence these test statistics have a permutation distribution th...
متن کامل