7,224 research outputs found
Distribution-Free Tests of Independence in High Dimensions
We consider the testing of mutual independence among all entries in a
-dimensional random vector based on independent observations. We study
two families of distribution-free test statistics, which include Kendall's tau
and Spearman's rho as important examples. We show that under the null
hypothesis the test statistics of these two families converge weakly to Gumbel
distributions, and propose tests that control the type I error in the
high-dimensional setting where . We further show that the two tests are
rate-optimal in terms of power against sparse alternatives, and outperform
competitors in simulations, especially when is large.Comment: to appear in Biometrik
Bootstrap and permutation tests of independence for point processes
Motivated by a neuroscience question about synchrony detection in spike train
analysis, we deal with the independence testing problem for point processes. We
introduce non-parametric test statistics, which are rescaled general
-statistics, whose corresponding critical values are constructed from
bootstrap and randomization/permutation approaches, making as few assumptions
as possible on the underlying distribution of the point processes. We derive
general consistency results for the bootstrap and for the permutation w.r.t. to
Wasserstein's metric, which induce weak convergence as well as convergence of
second order moments. The obtained bootstrap or permutation independence tests
are thus proved to be asymptotically of the prescribed size, and to be
consistent against any reasonable alternative. A simulation study is performed
to illustrate the derived theoretical results, and to compare the performance
of our new tests with existing ones in the neuroscientific literature
Tests of Independence in Separable Econometric Models: Theory and Application
A common stochastic restriction in econometric models separable in the latent variables is the assumption of stochastic independence between the unobserved and observed exogenous variables. Both simple and composite tests of this assumption are derived from properties of independence empirical processes and the consistency of these tests is established. As an application, we simulate estimation of a random quasilinear utility function, where we apply our tests of independence.Cramer-von Mises distance, Empirical independence processes, Random utility models, Semiparametric econometric models, Specification test of independence
Tests of Independence in Separable Econometric Models: Theory and Application
A common stochastic restriction in econometric models separable in the latent variables is the assumption of stochastic independence between the unobserved and observed exogenous variables. Both simple and composite tests of this assumption are derived from properties of independence empirical processes and the consistency of these tests is established. As an application, we simulate estimation of a random quasilinear utility function, where we apply our tests of independence.Cramer–von Mises distance, Empirical independence processes, Random utility models, Semiparametric econometric models, Specification test of independence
Tests of Independence in Contingency Tables
This report is a survey of the literature for a combination of different tests for both two-way and multi-way tests of independence in contingency tables. The derivation of the commonly used chi-square statistic for the tests will be shown immediately below, then followed by the summary of the different tests which will be the contents of this report
On Flexible Tests of Independence and homoscedasticity
Consider the nonparametric regression model Y = m(X) + τ(X)ε , where X and ε are independent random variables, ε has a mean of zero and variance σ2, τ is some unknown function used to model heteroscedasticity, and m(X) is an unknown function reflecting some conditional measure of location associated with Y, given X. Detecting dependence, by testing the hypothesis that m(X) does not vary with X, has the potential of being more sensitive to a wider range of associations compared to using Pearson\u27s correlation. This note has two goals. The first is to point out situations where a certain variation of an extant test of this hypothesis fails to control the probability of a Type I error, but another variation avoids this problem. The successful variation provides a new test of H0:τ(X) ≡ 1, the hypothesis that the error term is homoscedastic, which has the potential of higher power versus a method recently studied by Wilcox (2006). The second goal is to report some simulation results on how this method performs
Tests of Independence in Separable Econometric Models
A common stochastic restriction in econometric models separable in the latent variables is the assumption of stochastic independence between the unobserved and observed exogenous variables. Both simple and composite tests of this assumption are derived from properties of independence empirical processes and the consistency of these tests is established.Cramer-von Mises distance, Empirical independence processes, Random utility models, Semiparametric econometric models, Specification test of independence
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