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
This paper presents an estimator of location vector based on one dimensional projection of high dimensional data.The properties of the new estimator including consistency,asymptotic normality and robustness are discus...This paper presents an estimator of location vector based on one dimensional projection of high dimensional data.The properties of the new estimator including consistency,asymptotic normality and robustness are discussed.It is proved that the estimator is not only strongly consistent and asymptotically normal but also with a breakdown point 1/2 and a bounded influence function.展开更多
In this paper, we study the local asymptotic behavior of the regression spline estimator in the framework of marginal semiparametric model. Similarly to Zhu, Fung and He (2008), we give explicit expression for the asy...In this paper, we study the local asymptotic behavior of the regression spline estimator in the framework of marginal semiparametric model. Similarly to Zhu, Fung and He (2008), we give explicit expression for the asymptotic bias of regression spline estimator for nonparametric function f. Our results also show that the asymptotic bias of the regression spline estimator does not depend on the working covariance matrix, which distinguishes the regression splines from the smoothing splines and the seemingly unrelated kernel. To understand the local bias result of the regression spline estimator, we show that the regression spline estimator can be obtained iteratively by applying the standard weighted least squares regression spline estimator to pseudo-observations. At each iteration, the bias of the estimator is unchanged and only the variance is updated.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.
文摘This paper presents an estimator of location vector based on one dimensional projection of high dimensional data.The properties of the new estimator including consistency,asymptotic normality and robustness are discussed.It is proved that the estimator is not only strongly consistent and asymptotically normal but also with a breakdown point 1/2 and a bounded influence function.
基金supported by National Natural Science Foundation of China (Grant Nos.10671038,10801039)Youth Science Foundation of Fudan University (Grant No.08FQ29)Shanghai Leading Academic Discipline Project (Grant No.B118)
文摘In this paper, we study the local asymptotic behavior of the regression spline estimator in the framework of marginal semiparametric model. Similarly to Zhu, Fung and He (2008), we give explicit expression for the asymptotic bias of regression spline estimator for nonparametric function f. Our results also show that the asymptotic bias of the regression spline estimator does not depend on the working covariance matrix, which distinguishes the regression splines from the smoothing splines and the seemingly unrelated kernel. To understand the local bias result of the regression spline estimator, we show that the regression spline estimator can be obtained iteratively by applying the standard weighted least squares regression spline estimator to pseudo-observations. At each iteration, the bias of the estimator is unchanged and only the variance is updated.
