This paper studies estimation in partial functional linear quantile regression in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables....This paper studies estimation in partial functional linear quantile regression in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables. The slope function is estimated by the functional principal component basis. The asymptotic distribution of the estimator of the vector of slope parameters is derived and the global convergence rate of the quantile estimator of unknown slope function is established under suitable norm. It is showed that this rate is optirnal in a minimax sense under some smoothness assumptions on the covariance kernel of the covariate and the slope function. The convergence rate of the mean squared prediction error for the proposed estimators is also established. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about Berkeley growth data is used to illustrate our proposed methodology.展开更多
We consider a gradient iteration algorithm for prediction of functional linear regression under the framework of reproducing kernel Hilbert spaces.In the algorithm,we use an early stopping technique,instead of the cla...We consider a gradient iteration algorithm for prediction of functional linear regression under the framework of reproducing kernel Hilbert spaces.In the algorithm,we use an early stopping technique,instead of the classical Tikhonov regularization,to prevent the iteration from an overfitting function.Under mild conditions,we obtain upper bounds,essentially matching the known minimax lower bounds,for excess prediction risk.An almost sure convergence is also established for the proposed algorithm.展开更多
We propose a dynamically integrated regression model to predict the price of online auctions,including the final price.Different from existing models,the proposed method uses not only the historical price but also the...We propose a dynamically integrated regression model to predict the price of online auctions,including the final price.Different from existing models,the proposed method uses not only the historical price but also the information from bidding time.Consequently,the prediction accuracy is improved compared with the existing methods.An estimation method based on B-spline approximation is proposed for the estimation and the inference of parameters and nonparametric functions in this model.The minimax rate of convergence for the prediction risk and large-sample results including the consistency and the asymptotic normality are established.Simulation studies verify the finite sample performance and the appealing prediction accuracy and robustness.Finally,when we apply our method to a 7-day auction of iPhone 6s during December 2015 and March 2016,the proposed method predicts the ending price with a much smaller error than the existing models.展开更多
Few studies focus on the application of functional data to the field of design-based survey sampling.In this paper,the scalar-onunction regression model-assisted method is proposed to estimate the finite population me...Few studies focus on the application of functional data to the field of design-based survey sampling.In this paper,the scalar-onunction regression model-assisted method is proposed to estimate the finite population means with auxiliary functional data information.The functional principal component method is used for the estimation of functional linear regression model.Our proposed functional linear regression model-assisted(FLR-assisted)estimator is asymptotically design-unbiased,consistent under mild conditions.Simulation experiments and real data analysis show that the FLR-assisted estimators are more efficient than the Horvitz-Thompson estimators under different sampling designs.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11071120)
文摘This paper studies estimation in partial functional linear quantile regression in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables. The slope function is estimated by the functional principal component basis. The asymptotic distribution of the estimator of the vector of slope parameters is derived and the global convergence rate of the quantile estimator of unknown slope function is established under suitable norm. It is showed that this rate is optirnal in a minimax sense under some smoothness assumptions on the covariance kernel of the covariate and the slope function. The convergence rate of the mean squared prediction error for the proposed estimators is also established. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about Berkeley growth data is used to illustrate our proposed methodology.
基金supported in part by National Natural Science Foundation of China(Grant No.11871438)supported in part by the HKRGC GRF Nos.12300218,12300519,17201020,17300021,C1013-21GF,C7004-21GFJoint NSFC-RGC N-HKU76921。
文摘We consider a gradient iteration algorithm for prediction of functional linear regression under the framework of reproducing kernel Hilbert spaces.In the algorithm,we use an early stopping technique,instead of the classical Tikhonov regularization,to prevent the iteration from an overfitting function.Under mild conditions,we obtain upper bounds,essentially matching the known minimax lower bounds,for excess prediction risk.An almost sure convergence is also established for the proposed algorithm.
基金supported by National Natural Science Foundation of China(Grant Nos.11528102 and 11571282)Fundamental Research Funds for the Central Universities of China(Grant Nos.JBK120509 and 14TD0046)supported by the National Science Foundation of USA(Grant No.DMS-1620898)。
文摘We propose a dynamically integrated regression model to predict the price of online auctions,including the final price.Different from existing models,the proposed method uses not only the historical price but also the information from bidding time.Consequently,the prediction accuracy is improved compared with the existing methods.An estimation method based on B-spline approximation is proposed for the estimation and the inference of parameters and nonparametric functions in this model.The minimax rate of convergence for the prediction risk and large-sample results including the consistency and the asymptotic normality are established.Simulation studies verify the finite sample performance and the appealing prediction accuracy and robustness.Finally,when we apply our method to a 7-day auction of iPhone 6s during December 2015 and March 2016,the proposed method predicts the ending price with a much smaller error than the existing models.
基金China Postdoctoral Science Foundation(Grant Nos.2021M691443,2021TQ0141)SUSTC Presidential Postdoctoral Fellow-ship.Huiming Zhang was supported in part by the University of Macao under UM Macao Talent Programme(UMMTP-2020-01).
文摘Few studies focus on the application of functional data to the field of design-based survey sampling.In this paper,the scalar-onunction regression model-assisted method is proposed to estimate the finite population means with auxiliary functional data information.The functional principal component method is used for the estimation of functional linear regression model.Our proposed functional linear regression model-assisted(FLR-assisted)estimator is asymptotically design-unbiased,consistent under mild conditions.Simulation experiments and real data analysis show that the FLR-assisted estimators are more efficient than the Horvitz-Thompson estimators under different sampling designs.
