8 research outputs found

    Testing conditional independence using maximal nonlinear conditional correlation

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    In this paper, the maximal nonlinear conditional correlation of two random vectors XX and YY given another random vector ZZ, denoted by ρ1(X,Y∣Z)\rho_1(X,Y|Z), is defined as a measure of conditional association, which satisfies certain desirable properties. When ZZ is continuous, a test for testing the conditional independence of XX and YY given ZZ is constructed based on the estimator of a weighted average of the form βˆ‘k=1nZfZ(zk)ρ12(X,Y∣Z=zk)\sum_{k=1}^{n_Z}f_Z(z_k)\rho^2_1(X,Y|Z=z_k), where fZf_Z is the probability density function of ZZ and the zkz_k's are some points in the range of ZZ. Under some conditions, it is shown that the test statistic is asymptotically normal under conditional independence, and the test is consistent.Comment: Published in at http://dx.doi.org/10.1214/09-AOS770 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Convergence rates for posterior distributions and adaptive estimation

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    The goal of this paper is to provide theorems on convergence rates of posterior distributions that can be applied to obtain good convergence rates in the context of density estimation as well as regression. We show how to choose priors so that the posterior distributions converge at the optimal rate without prior knowledge of the degree of smoothness of the density function or the regression function to be estimated.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/00905360400000049

    A conditional independence test for dependent data based on maximal conditional correlation

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    AbstractIn Huang (2010)Β [8], a test of conditional independence based on maximal nonlinear conditional correlation is proposed and the asymptotic distribution for the test statistic under conditional independence is established for IID data. In this paper, we derive the asymptotic distribution for the test statistic under conditional independence for Ξ±-mixing data. The results of simulation show that the test performs reasonably well for dependent data. We also apply the test to stock index data to test Granger noncausality between returns and trading volume

    A mixture logistic model for panel data with a Markov structure

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    In this study, we propose a mixture logistic regression model with a Markov structure, and consider the estimation of model parameters using maximum likelihood estimation. We also provide a forward type variable selection algorithm to choose the important explanatory variables to reduce the number of parameters in the proposed model.Comment: Some results of this study have been included in the report of a research project of Professor Yu-Hsiang Cheng, and the report is now available. Thus we add the information in this versio

    Estimating the parametric component of nonlinear partial spline model

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    Consider a nonlinear partial spline model . This article studies the estimation problem of when g0 is approximated by some graduating function. Some asymptotic results for are derived. In particular, it is shown that can be estimated with the usual parametric convergence rate without undersmoothing g0.Additive models Method of sieves Semiparametric regression models Nonlinear regression