The varying-coefficient partially linear regression model is proposed by combining nonparametric and varying-coefficient regression procedures. Wong, et al. （2008） proposed the model and gave its estimation by the l...The varying-coefficient partially linear regression model is proposed by combining nonparametric and varying-coefficient regression procedures. Wong, et al. （2008） proposed the model and gave its estimation by the local linear method. In this paper its inference is addressed. Based on these estimates, the generalized like- lihood ratio test is established. Under the null hypotheses the normalized test statistic follows a x2-distribution asymptotically, with the scale constant and the degrees of freedom being independent of the nuisance param- eters. This is the Wilks phenomenon. Furthermore its asymptotic power is also derived, which achieves the optimal rate of convergence for nonparametric hypotheses testing. A simulation and a real example are used to evaluate the performances of the testing procedures empirically.展开更多
There has been a rapid progress in designing valid and effective statisticalhypothesis tests for the order of a finite mixture model.In particular,EM-test forthe order of the mixture model has been developed and found...There has been a rapid progress in designing valid and effective statisticalhypothesis tests for the order of a finite mixture model.In particular,EM-test forthe order of the mixture model has been developed and found effective when thecomponent distribution contains a single parameter.EM-test is found to be particularlyeffective and elegant for the order of normal mixture in both mean and variance.Theidea behind EM-test has been found widely applicable.In this paper,we investigatethe use of EM-test for the order of a finite normal mixture in the mean parameterwith equal but unknown component variances.We show that for any positive integermo≥2,the limiting distribution of the EM-test for the order of mo against the higherorder alternative is x^(5)_(m0-1).A genetic example is used to illustrate the application ofthe EM-test.展开更多
基金supported in part by National Natural Science Foundation of China(11171112,11201190)Doctoral Fund of Ministry of Education of China(20130076110004)+1 种基金Program of Shanghai Subject Chief Scientist(14XD1401600)the 111 Project of China(B14019)
文摘The varying-coefficient partially linear regression model is proposed by combining nonparametric and varying-coefficient regression procedures. Wong, et al. （2008） proposed the model and gave its estimation by the local linear method. In this paper its inference is addressed. Based on these estimates, the generalized like- lihood ratio test is established. Under the null hypotheses the normalized test statistic follows a x2-distribution asymptotically, with the scale constant and the degrees of freedom being independent of the nuisance param- eters. This is the Wilks phenomenon. Furthermore its asymptotic power is also derived, which achieves the optimal rate of convergence for nonparametric hypotheses testing. A simulation and a real example are used to evaluate the performances of the testing procedures empirically.
文摘There has been a rapid progress in designing valid and effective statisticalhypothesis tests for the order of a finite mixture model.In particular,EM-test forthe order of the mixture model has been developed and found effective when thecomponent distribution contains a single parameter.EM-test is found to be particularlyeffective and elegant for the order of normal mixture in both mean and variance.Theidea behind EM-test has been found widely applicable.In this paper,we investigatethe use of EM-test for the order of a finite normal mixture in the mean parameterwith equal but unknown component variances.We show that for any positive integermo≥2,the limiting distribution of the EM-test for the order of mo against the higherorder alternative is x^(5)_(m0-1).A genetic example is used to illustrate the application ofthe EM-test.
