Abstract In this paper, the estimation method based on the “generalized profile likelihood” for the conditionally parametric models in the paper given by Severini and Wong (1992) is extended to fixed design semipara...Abstract In this paper, the estimation method based on the “generalized profile likelihood” for the conditionally parametric models in the paper given by Severini and Wong (1992) is extended to fixed design semiparametric nonlinear regression models.For these semiparametric nonlinear regression models,the resulting estimator of parametric component of the model is shown to be asymptotically efficient and the strong convergence rate of nonparametric component is investigated.Many results (for example Chen (1988),Gao & Zhao (1993), Rice (1986) et al.) are extended to fixed design semiparametric nonlinear regression models.展开更多
Varying-coefficient models with longitudinal observations are very useful in epidemiology and some other practical fields.In this paper,a reducing component procedure is proposed for es- timating the unknown functions...Varying-coefficient models with longitudinal observations are very useful in epidemiology and some other practical fields.In this paper,a reducing component procedure is proposed for es- timating the unknown functions and their derivatives in very general models,in which the unknown coefficient functions admit different or the same degrees of smoothness and the covariates can be time- dependent.The asymptotic properties of the estimators,such as consistency,rate of convergence and asymptotic distribution,are derived.The asymptotic results show that the asymptotic variance of the reducing component estimators is smaller than that of the existing estimators when the coefficient functions admit different degrees of smoothness.Finite sample properties of our procedures are studied through Monte Carlo simulations.展开更多
Regression splines are often used for fitting nonparametric functions, and they work especially well for additivity models. In this paper, we consider two simple tests of additivity: an adaptation of Tukey’s one degr...Regression splines are often used for fitting nonparametric functions, and they work especially well for additivity models. In this paper, we consider two simple tests of additivity: an adaptation of Tukey’s one degree of freedom test and a nonparametric version of Rao’s score test. While the Tukey-type test can detect most forms of the local non-additivity at the parametric rate of O(n-1/2), the score test is consistent for all alternative at a nonparametric rate. The asymptotic distribution of these test statistics is derived under both the null and local alternative hypotheses. A simulation study is conducted to compare their finite-sample performances with some existing kernel-based tests. The score test is found to have a good overall performance.展开更多
文摘Abstract In this paper, the estimation method based on the “generalized profile likelihood” for the conditionally parametric models in the paper given by Severini and Wong (1992) is extended to fixed design semiparametric nonlinear regression models.For these semiparametric nonlinear regression models,the resulting estimator of parametric component of the model is shown to be asymptotically efficient and the strong convergence rate of nonparametric component is investigated.Many results (for example Chen (1988),Gao & Zhao (1993), Rice (1986) et al.) are extended to fixed design semiparametric nonlinear regression models.
基金Research Foundation for Doctor Programme (Grant No.20060254006)the National Natural Science Foundation of China (Grant No.10671089)
文摘Varying-coefficient models with longitudinal observations are very useful in epidemiology and some other practical fields.In this paper,a reducing component procedure is proposed for es- timating the unknown functions and their derivatives in very general models,in which the unknown coefficient functions admit different or the same degrees of smoothness and the covariates can be time- dependent.The asymptotic properties of the estimators,such as consistency,rate of convergence and asymptotic distribution,are derived.The asymptotic results show that the asymptotic variance of the reducing component estimators is smaller than that of the existing estimators when the coefficient functions admit different degrees of smoothness.Finite sample properties of our procedures are studied through Monte Carlo simulations.
基金This work was partially supported by the National Natural Science Foundation of China (Grant No. 10231030)the Excellent Young Teacher Foundation of Education Ministry of China and University of Illinois Campus Research Board and by NSF Award SBR-9617278 and DMS-0102411
文摘Regression splines are often used for fitting nonparametric functions, and they work especially well for additivity models. In this paper, we consider two simple tests of additivity: an adaptation of Tukey’s one degree of freedom test and a nonparametric version of Rao’s score test. While the Tukey-type test can detect most forms of the local non-additivity at the parametric rate of O(n-1/2), the score test is consistent for all alternative at a nonparametric rate. The asymptotic distribution of these test statistics is derived under both the null and local alternative hypotheses. A simulation study is conducted to compare their finite-sample performances with some existing kernel-based tests. The score test is found to have a good overall performance.
