In this paper, based on the theory of parameter estimation, we give a selection method and, in a sense of a good character of the parameter estimation, we think that it is very reasonable. Moreover, we offer a calcula...In this paper, based on the theory of parameter estimation, we give a selection method and, in a sense of a good character of the parameter estimation, we think that it is very reasonable. Moreover, we offer a calculation method of selection statistic and an applied example.展开更多
Demand response has gained significant attention recently with the increasing penetration of renewable energy sources in power systems. Air conditioning loads are typical thermostatically controlled loads which can pl...Demand response has gained significant attention recently with the increasing penetration of renewable energy sources in power systems. Air conditioning loads are typical thermostatically controlled loads which can play an active role in ancillary services by regulating their aggregated power consumption. The aggregation of air conditioners is essential to the control of air conditioning loads. In this paper, linear state equations are proposed to aggregate air conditioning loads by solving coupled Fokker–Planck equations(CFPEs) using the finite difference method. By analyzing the numerical stability and convergence of the difference scheme, the grid spacings, including temperature step and time step, are properly determined according to the maximal principle. Stationary solutions of the CFPEs are obtained by analytical and numerical methods. Furthermore, a classification method using dimension reduction is proposed to deal with the problem of heterogeneous parameters and interval estimation is applied to describe the stochastic behavior of air conditioning loads. The simulation results verify the effectiveness of the proposed methods.展开更多
The Bayesian method is applied to the joint model selection and parameter estimation problem of the GTD model. An algorithm based on RJ-MCMC is designed. This algorithm not only improves the model order selection and ...The Bayesian method is applied to the joint model selection and parameter estimation problem of the GTD model. An algorithm based on RJ-MCMC is designed. This algorithm not only improves the model order selection and parameter estimation accuracy by exploiting the priori information of the GTD model, but also solves the mixed parameter estimation problem of the GTD model properly. Its performance is tested using numerical simulations and data generated by electromagnetic code. It is shown that it gives good model order selection and parameter estimation results, especially for low SNR, closely-spaced components and short data situations.展开更多
The spatial and spatiotemporal autoregressive conditional heteroscedasticity(STARCH) models receive increasing attention. In this paper, we introduce a spatiotemporal autoregressive(STAR) model with STARCH errors, whi...The spatial and spatiotemporal autoregressive conditional heteroscedasticity(STARCH) models receive increasing attention. In this paper, we introduce a spatiotemporal autoregressive(STAR) model with STARCH errors, which can capture the spatiotemporal dependence in mean and variance simultaneously. The Bayesian estimation and model selection are considered for our model. By Monte Carlo simulations, it is shown that the Bayesian estimator performs better than the corresponding maximum-likelihood estimator, and the Bayesian model selection can select out the true model in most times. Finally, two empirical examples are given to illustrate the superiority of our models in fitting those data.展开更多
Based on the double penalized estimation method,a new variable selection procedure is proposed for partially linear models with longitudinal data.The proposed procedure can avoid the effects of the nonparametric estim...Based on the double penalized estimation method,a new variable selection procedure is proposed for partially linear models with longitudinal data.The proposed procedure can avoid the effects of the nonparametric estimator on the variable selection for the parameters components.Under some regularity conditions,the rate of convergence and asymptotic normality of the resulting estimators are established.In addition,to improve efficiency for regression coefficients,the estimation of the working covariance matrix is involved in the proposed iterative algorithm.Some simulation studies are carried out to demonstrate that the proposed method performs well.展开更多
Highly Active Antiretroviral Therapy (HAART) has changed the course of human immunodeficiency virus (HIV) treatments since its introduction. However, for many patients, long term continuous HAART is expensive and can ...Highly Active Antiretroviral Therapy (HAART) has changed the course of human immunodeficiency virus (HIV) treatments since its introduction. However, for many patients, long term continuous HAART is expensive and can include problems with drug toxicity and side effects, as well as increased drug resistance. Because of these reasons, some HIV infected patients will voluntarily terminate HAART. Some of these patients will also interrupt the continuous prescribed therapies for short or long periods. After discontinuing HAART, patients will usually experience a rapid increase in viral load coupled with an immediate decline in CD4+ counts. The canonical example of a patient undergoing unsupervised breaks in HAART is that of the “Berlin patient”. In this case, the patient was able to control viral load in the absence of treatment by cycling HAART on and off due to non-related infections. Due to this patient, interest in the use of structured treatment interruptions (STI) as a mechanism to regulate an HIV infection piqued. This paper describes an optimal control approach to determine STI regimen for HIV patients. The optimal STI was implemented in the context of the receding horizon control (RHC) using a mathematical model for the in-vivo dynamics of an HIV type 1 infection. Using available clinical data, we calibrate the model by estimating on a patient specific basis, a best estimable set of parameters using sensitivity analysis and subset selection. We demonstrate how customized STI protocols can be designed through the variation of control parameters on a patient specific basis.展开更多
In this paper, we consider the issue of variable selection in partial linear single-index models under the assumption that the vector of regression coefficients is sparse. We apply penalized spline to estimate the non...In this paper, we consider the issue of variable selection in partial linear single-index models under the assumption that the vector of regression coefficients is sparse. We apply penalized spline to estimate the nonparametric function and SCAD penalty to achieve sparse estimates of regression parameters in both the linear and single-index parts of the model. Under some mild conditions, it is shown that the penalized estimators have oracle property, in the sense that it is asymptotically normal with the same mean and covariance that they would have if zero coefficients are known in advance. Our model owns a least square representation, therefore standard least square programming algorithms can be implemented without extra programming efforts. In the meantime, parametric estimation, variable selection and nonparametric estimation can be realized in one step, which incredibly increases computational stability. The finite sample performance of the penalized estimators is evaluated through Monte Carlo studies and illustrated with a real data set.展开更多
基金Supported by the Natural Science Foundation of Anhui Education Committee
文摘In this paper, based on the theory of parameter estimation, we give a selection method and, in a sense of a good character of the parameter estimation, we think that it is very reasonable. Moreover, we offer a calculation method of selection statistic and an applied example.
基金supported by National Natural Science Foundation of China(No.51177093)
文摘Demand response has gained significant attention recently with the increasing penetration of renewable energy sources in power systems. Air conditioning loads are typical thermostatically controlled loads which can play an active role in ancillary services by regulating their aggregated power consumption. The aggregation of air conditioners is essential to the control of air conditioning loads. In this paper, linear state equations are proposed to aggregate air conditioning loads by solving coupled Fokker–Planck equations(CFPEs) using the finite difference method. By analyzing the numerical stability and convergence of the difference scheme, the grid spacings, including temperature step and time step, are properly determined according to the maximal principle. Stationary solutions of the CFPEs are obtained by analytical and numerical methods. Furthermore, a classification method using dimension reduction is proposed to deal with the problem of heterogeneous parameters and interval estimation is applied to describe the stochastic behavior of air conditioning loads. The simulation results verify the effectiveness of the proposed methods.
基金Supported by the National "973" Key Basic Research Project (Grant No. 51314)
文摘The Bayesian method is applied to the joint model selection and parameter estimation problem of the GTD model. An algorithm based on RJ-MCMC is designed. This algorithm not only improves the model order selection and parameter estimation accuracy by exploiting the priori information of the GTD model, but also solves the mixed parameter estimation problem of the GTD model properly. Its performance is tested using numerical simulations and data generated by electromagnetic code. It is shown that it gives good model order selection and parameter estimation results, especially for low SNR, closely-spaced components and short data situations.
基金supported by National Natural Science Foundation of China (No.12271206)Natural Science Foundation of Jilin Province (No.20210101143JC)Science and Technology Research Planning Project of Jilin Provincial Department of Education (No.JJKH20231122KJ)。
文摘The spatial and spatiotemporal autoregressive conditional heteroscedasticity(STARCH) models receive increasing attention. In this paper, we introduce a spatiotemporal autoregressive(STAR) model with STARCH errors, which can capture the spatiotemporal dependence in mean and variance simultaneously. The Bayesian estimation and model selection are considered for our model. By Monte Carlo simulations, it is shown that the Bayesian estimator performs better than the corresponding maximum-likelihood estimator, and the Bayesian model selection can select out the true model in most times. Finally, two empirical examples are given to illustrate the superiority of our models in fitting those data.
基金Supported by National Natural Science Foundation of China(Grant No.11101119)the Training Program for Excellent Young Teachers in Guangxi Universitiesthe Philosophy and Social Sciences Foundation of Guangxi(Grant No.11FTJ002)
文摘Based on the double penalized estimation method,a new variable selection procedure is proposed for partially linear models with longitudinal data.The proposed procedure can avoid the effects of the nonparametric estimator on the variable selection for the parameters components.Under some regularity conditions,the rate of convergence and asymptotic normality of the resulting estimators are established.In addition,to improve efficiency for regression coefficients,the estimation of the working covariance matrix is involved in the proposed iterative algorithm.Some simulation studies are carried out to demonstrate that the proposed method performs well.
文摘Highly Active Antiretroviral Therapy (HAART) has changed the course of human immunodeficiency virus (HIV) treatments since its introduction. However, for many patients, long term continuous HAART is expensive and can include problems with drug toxicity and side effects, as well as increased drug resistance. Because of these reasons, some HIV infected patients will voluntarily terminate HAART. Some of these patients will also interrupt the continuous prescribed therapies for short or long periods. After discontinuing HAART, patients will usually experience a rapid increase in viral load coupled with an immediate decline in CD4+ counts. The canonical example of a patient undergoing unsupervised breaks in HAART is that of the “Berlin patient”. In this case, the patient was able to control viral load in the absence of treatment by cycling HAART on and off due to non-related infections. Due to this patient, interest in the use of structured treatment interruptions (STI) as a mechanism to regulate an HIV infection piqued. This paper describes an optimal control approach to determine STI regimen for HIV patients. The optimal STI was implemented in the context of the receding horizon control (RHC) using a mathematical model for the in-vivo dynamics of an HIV type 1 infection. Using available clinical data, we calibrate the model by estimating on a patient specific basis, a best estimable set of parameters using sensitivity analysis and subset selection. We demonstrate how customized STI protocols can be designed through the variation of control parameters on a patient specific basis.
基金Supported by the National Natural Science Foundation of China(No.11671096)
文摘In this paper, we consider the issue of variable selection in partial linear single-index models under the assumption that the vector of regression coefficients is sparse. We apply penalized spline to estimate the nonparametric function and SCAD penalty to achieve sparse estimates of regression parameters in both the linear and single-index parts of the model. Under some mild conditions, it is shown that the penalized estimators have oracle property, in the sense that it is asymptotically normal with the same mean and covariance that they would have if zero coefficients are known in advance. Our model owns a least square representation, therefore standard least square programming algorithms can be implemented without extra programming efforts. In the meantime, parametric estimation, variable selection and nonparametric estimation can be realized in one step, which incredibly increases computational stability. The finite sample performance of the penalized estimators is evaluated through Monte Carlo studies and illustrated with a real data set.
