In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the l...In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.展开更多
The Cox proportional hazard model is being used extensively in oncology in studying the relationship between survival times and prognostic factors. The main question that needs to be addressed with respect to the appl...The Cox proportional hazard model is being used extensively in oncology in studying the relationship between survival times and prognostic factors. The main question that needs to be addressed with respect to the applicability of the Cox PH model is whether the proportional hazard assumption is met. Failure to justify the subject assumption will lead to misleading results. In addition, identifying the correct functional form of the continuous covariates is an important aspect in the development of a Cox proportional hazard model. The purpose of this study is to develop an extended Cox regression model for breast cancer survival data which takes non-proportional hazards and non-linear effects that exist in prognostic factors into consideration. Non-proportional hazards and non-linear effects are detected using methods based on residuals. An extended Cox model with non-linear effects and time-varying effects is proposed to adjust the Cox proportional hazard model. Age and tumor size were found to have nonlinear effects. Progesterone receptor assay status and age violated the proportional hazard assumption in the Cox model. Quadratic effect of age and progesterone receptor assay status had hazard ratio that changes with time. We have introduced a statistical model to overcome the presence of the proportional hazard assumption violation for the Cox proportional hazard model for breast cancer data. The proposed extended model considers the time varying nature of the hazard ratio and non-linear effects of the covariates. Our improved Cox model gives a better insight on the hazard rates associated with the breast cancer risk factors.展开更多
The quantile estimation methods are proposed for functional-coefficient partially linear regression （FCPLR） model by combining nonparametric and functional-coefficient regression （FCR） model. The local linear sche...The quantile estimation methods are proposed for functional-coefficient partially linear regression （FCPLR） model by combining nonparametric and functional-coefficient regression （FCR） model. The local linear scheme and the integrated method are used to obtain Focal quantile estimators of all unknown functions in the FCPLR model. These resulting estimators are asymptotically normal, but each of them has big variance. To reduce variances of these quantile estimators, the one-step backfitting technique is used to obtain the efficient quantile estimators of all unknown functions, and their asymptotic normalities are derived. Two simulated examples are carried out to illustrate the proposed estimation methodology.展开更多
A continuous-time Model Predictive Controller was proposed using Kautz function in order to improve the performance of Load Frequency Control(LFC).A dynamic model of an interconnected power system was used for Model P...A continuous-time Model Predictive Controller was proposed using Kautz function in order to improve the performance of Load Frequency Control(LFC).A dynamic model of an interconnected power system was used for Model Predictive Controller(MPC)design.MPC predicts the future trajectory of the dynamic model by calculating the optimal closed loop feedback gain matrix.In this paper,the optimal closed loop feedback gain matrix was calculated using Kautz function.Being an Orthonormal Basis Function(OBF),Kautz function has an advantage of solving complex pole-based nonlinear system.Genetic Algorithm(GA)was applied to optimally tune the Kautz function-based MPC.A constraint based on phase plane analysis was implemented with the cost function in order to improve the robustness of the Kautz function-based MPC.The proposed method was simulated with three area interconnected power system and the efficiency of the proposed method was measured and exhibited by comparing with conventional Proportional and Integral(PI)controller and Linear Quadratic Regulation(LQR).展开更多
文摘In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.
文摘The Cox proportional hazard model is being used extensively in oncology in studying the relationship between survival times and prognostic factors. The main question that needs to be addressed with respect to the applicability of the Cox PH model is whether the proportional hazard assumption is met. Failure to justify the subject assumption will lead to misleading results. In addition, identifying the correct functional form of the continuous covariates is an important aspect in the development of a Cox proportional hazard model. The purpose of this study is to develop an extended Cox regression model for breast cancer survival data which takes non-proportional hazards and non-linear effects that exist in prognostic factors into consideration. Non-proportional hazards and non-linear effects are detected using methods based on residuals. An extended Cox model with non-linear effects and time-varying effects is proposed to adjust the Cox proportional hazard model. Age and tumor size were found to have nonlinear effects. Progesterone receptor assay status and age violated the proportional hazard assumption in the Cox model. Quadratic effect of age and progesterone receptor assay status had hazard ratio that changes with time. We have introduced a statistical model to overcome the presence of the proportional hazard assumption violation for the Cox proportional hazard model for breast cancer data. The proposed extended model considers the time varying nature of the hazard ratio and non-linear effects of the covariates. Our improved Cox model gives a better insight on the hazard rates associated with the breast cancer risk factors.
基金supported by the Zhejiang Provincial Natural Science Foundation of China (No. Y6110662)
文摘The quantile estimation methods are proposed for functional-coefficient partially linear regression （FCPLR） model by combining nonparametric and functional-coefficient regression （FCR） model. The local linear scheme and the integrated method are used to obtain Focal quantile estimators of all unknown functions in the FCPLR model. These resulting estimators are asymptotically normal, but each of them has big variance. To reduce variances of these quantile estimators, the one-step backfitting technique is used to obtain the efficient quantile estimators of all unknown functions, and their asymptotic normalities are derived. Two simulated examples are carried out to illustrate the proposed estimation methodology.
文摘A continuous-time Model Predictive Controller was proposed using Kautz function in order to improve the performance of Load Frequency Control(LFC).A dynamic model of an interconnected power system was used for Model Predictive Controller(MPC)design.MPC predicts the future trajectory of the dynamic model by calculating the optimal closed loop feedback gain matrix.In this paper,the optimal closed loop feedback gain matrix was calculated using Kautz function.Being an Orthonormal Basis Function(OBF),Kautz function has an advantage of solving complex pole-based nonlinear system.Genetic Algorithm(GA)was applied to optimally tune the Kautz function-based MPC.A constraint based on phase plane analysis was implemented with the cost function in order to improve the robustness of the Kautz function-based MPC.The proposed method was simulated with three area interconnected power system and the efficiency of the proposed method was measured and exhibited by comparing with conventional Proportional and Integral(PI)controller and Linear Quadratic Regulation(LQR).
