Distance-based regression model,as a nonparametric multivariate method,has been widely used to detect the association between variations in a distance or dissimilarity matrix for outcomes and predictor variables of in...Distance-based regression model,as a nonparametric multivariate method,has been widely used to detect the association between variations in a distance or dissimilarity matrix for outcomes and predictor variables of interest in genetic association studies,genomic analyses,and many other research areas.Based on it,a pseudo-F statistic which partitions the variation in distance matrices is often constructed to achieve the aim.To the best of our knowledge,the statistical properties of the pseudo-F statistic has not yet been well established in the literature.To fill this gap,the authors study the asymptotic null distribution of the pseudo-F statistic and show that it is asymptotically equivalent to a mixture of chi-squared random variables.Given that the pseudo-F test statistic has unsatisfactory power when the correlations of the response variables are large,the authors propose a square-root F-type test statistic which replaces the similarity matrix with its square root.The asymptotic null distribution of the new test statistic and power of both tests are also investigated.Simulation studies are conducted to validate the asymptotic distributions of the tests and demonstrate that the proposed test has more robust power than the pseudo-F test.Both test statistics are exemplified with a gene expression dataset for a prostate cancer pathway.展开更多
In goodness-of-fit tests, Pearson＇s chi-squared test is one of most widely used tools of formal statistical analysis. However, Pearson＇s chi-squared test depends on the partition of the sample space. Different const...In goodness-of-fit tests, Pearson＇s chi-squared test is one of most widely used tools of formal statistical analysis. However, Pearson＇s chi-squared test depends on the partition of the sample space. Different constructions of the partition of the sample space may lead to different conclusions. Based on an equiprobable partition of sample space, a modified chi^quared test is proposed. A method for constructing the modified chi-squared test is proposed. As an application, the proposed test is used to test whether vectorial data come from an uniformity distribution defined on the hypersphere. Some simulation studies show that the modified chisquared test against different alternative is robust.展开更多
The author examines six age-group specific suicide rates in 2016 between states (in the continental United States) with and without professional sports teams in baseball [MLB], football [NFL], hockey [NHL], and basket...The author examines six age-group specific suicide rates in 2016 between states (in the continental United States) with and without professional sports teams in baseball [MLB], football [NFL], hockey [NHL], and basketball [NBA]. States with at least one team in baseball or football have significantly lower suicide rates among adults in all six age groups (over 20 years of age). States with at least one hockey team have significantly lower suicide rates for all adults over the age of 20, except the oldest age group (adults 65 years of age or over). The results are weakest for states with at least one basketball team. Adults only between 25 and 44 years of age and 65 years of age or over have significantly lower suicide rates with at least one NBA team.展开更多
In this paper, we consider testing the hypothesis that all multinomial populations in the stratified contingency table are identically distributed against the alternative that all these popula- tions are in simple tre...In this paper, we consider testing the hypothesis that all multinomial populations in the stratified contingency table are identically distributed against the alternative that all these popula- tions are in simple tree order. We provide an asymptotic represen- tation of the order-restricted maximum likelihood estimate of the unknown parameters. The resulting estimators are proven to be ~n-consistent and asymptotically normal under appropriate conditions. A chi-squared test method is used for this hypothesis test problem. A real data set is applied to illustrate our theoretical result.展开更多
The classical chi-squared goodness of fit test assumes the number of classes is fixed,meanwhile the test statistic has a limiting chi-square distribution under the null hypothesis.It is well known that the number of c...The classical chi-squared goodness of fit test assumes the number of classes is fixed,meanwhile the test statistic has a limiting chi-square distribution under the null hypothesis.It is well known that the number of classes varying with sample size in the test has attached more and more attention.However,in this situation,there is not theoretical results for the asymptotic property of such chi-squared test statistic.This paper proves the consistency of chi-squared test with varying number of classes under some conditions.Meanwhile,the authors also give a convergence rate of KolmogorovSimirnov distance between the test statistic and corresponding chi-square distributed random variable.In addition,a real example and simulation results validate the reasonability of theoretical result and the superiority of chi-squared test with varying number of classes.展开更多
基金partially supported by Beijing Natural Science Foundation under Grant No.Z180006.
文摘Distance-based regression model,as a nonparametric multivariate method,has been widely used to detect the association between variations in a distance or dissimilarity matrix for outcomes and predictor variables of interest in genetic association studies,genomic analyses,and many other research areas.Based on it,a pseudo-F statistic which partitions the variation in distance matrices is often constructed to achieve the aim.To the best of our knowledge,the statistical properties of the pseudo-F statistic has not yet been well established in the literature.To fill this gap,the authors study the asymptotic null distribution of the pseudo-F statistic and show that it is asymptotically equivalent to a mixture of chi-squared random variables.Given that the pseudo-F test statistic has unsatisfactory power when the correlations of the response variables are large,the authors propose a square-root F-type test statistic which replaces the similarity matrix with its square root.The asymptotic null distribution of the new test statistic and power of both tests are also investigated.Simulation studies are conducted to validate the asymptotic distributions of the tests and demonstrate that the proposed test has more robust power than the pseudo-F test.Both test statistics are exemplified with a gene expression dataset for a prostate cancer pathway.
基金Foundation item： the Natural Science Foundation of Beijing （No. 1062001）Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality（No. 05006011200702）.Acknowledgements The authors cordially thank the Associate Editor and Reviewers for their constructive comments which lead to improvement of the manuscript. They are also very grateful to Prof. Adelaide Figueiredo for his help.
文摘In goodness-of-fit tests, Pearson＇s chi-squared test is one of most widely used tools of formal statistical analysis. However, Pearson＇s chi-squared test depends on the partition of the sample space. Different constructions of the partition of the sample space may lead to different conclusions. Based on an equiprobable partition of sample space, a modified chi^quared test is proposed. A method for constructing the modified chi-squared test is proposed. As an application, the proposed test is used to test whether vectorial data come from an uniformity distribution defined on the hypersphere. Some simulation studies show that the modified chisquared test against different alternative is robust.
文摘The author examines six age-group specific suicide rates in 2016 between states (in the continental United States) with and without professional sports teams in baseball [MLB], football [NFL], hockey [NHL], and basketball [NBA]. States with at least one team in baseball or football have significantly lower suicide rates among adults in all six age groups (over 20 years of age). States with at least one hockey team have significantly lower suicide rates for all adults over the age of 20, except the oldest age group (adults 65 years of age or over). The results are weakest for states with at least one basketball team. Adults only between 25 and 44 years of age and 65 years of age or over have significantly lower suicide rates with at least one NBA team.
基金Supported by the National Natural Science Foundation of China (10771163)
文摘In this paper, we consider testing the hypothesis that all multinomial populations in the stratified contingency table are identically distributed against the alternative that all these popula- tions are in simple tree order. We provide an asymptotic represen- tation of the order-restricted maximum likelihood estimate of the unknown parameters. The resulting estimators are proven to be ~n-consistent and asymptotically normal under appropriate conditions. A chi-squared test method is used for this hypothesis test problem. A real data set is applied to illustrate our theoretical result.
基金supported by the Natural Science Foundation of China under Grant Nos.11071022,11028103,11231010,11471223,BCMIISthe Beijing Municipal Educational Commission Foundation under Grant Nos.KZ201410028030,KM201210028005Jishou University Subject in 2014(No:14JD035)
文摘The classical chi-squared goodness of fit test assumes the number of classes is fixed,meanwhile the test statistic has a limiting chi-square distribution under the null hypothesis.It is well known that the number of classes varying with sample size in the test has attached more and more attention.However,in this situation,there is not theoretical results for the asymptotic property of such chi-squared test statistic.This paper proves the consistency of chi-squared test with varying number of classes under some conditions.Meanwhile,the authors also give a convergence rate of KolmogorovSimirnov distance between the test statistic and corresponding chi-square distributed random variable.In addition,a real example and simulation results validate the reasonability of theoretical result and the superiority of chi-squared test with varying number of classes.
