This paper is focused on the goodness-of-fit test of the functional linear composite quantile regression model.A nonparametric test is proposed by using the orthogonality of the residual and its conditional expectatio...This paper is focused on the goodness-of-fit test of the functional linear composite quantile regression model.A nonparametric test is proposed by using the orthogonality of the residual and its conditional expectation under the null model.The proposed test statistic has an asymptotic standard normal distribution under the null hypothesis,and tends to infinity in probability under the alternative hypothesis,which implies the consistency of the test.Furthermore,it is proved that the test statistic converges to a normal distribution with nonzero mean under a local alternative hypothesis.Extensive simulations are reported,and the results show that the proposed test has proper sizes and is sensitive to the considered model discrepancies.The proposed methods are also applied to two real datasets.展开更多
This paper considers the estimation of a semiparametric isotonic regression model when the covariates are measured with additive errors and the response is randomly right censored by a censoring time.The authors show ...This paper considers the estimation of a semiparametric isotonic regression model when the covariates are measured with additive errors and the response is randomly right censored by a censoring time.The authors show that the proposed estimator of the regression parameter is rootn consistent and asymptotically normal.The authors also show that the isotonic estimator of the functional component,at a fixed point,is cubic root-n consistent and converges in distribution to the slope at zero of the greatest convex minorant of the sum of a two-sided standard Brownian motion and the square of the time parameter.A simulation study is carried out to investigate the performance of the estimators proposed in this article.展开更多
Linear regression models for interval-valued data have been widely studied.Most literatures are to split an interval into two real numbers,i.e.,the left-and right-endpoints or the center and radius of this interval,an...Linear regression models for interval-valued data have been widely studied.Most literatures are to split an interval into two real numbers,i.e.,the left-and right-endpoints or the center and radius of this interval,and fit two separate real-valued or two dimension linear regression models.This paper is focused on the bias-corrected and heteroscedasticity-adjusted modeling by imposing order constraint to the endpoints of the response interval and weighted linear least squares with estimated covariance matrix,based on a generalized linear model for interval-valued data.A three step estimation method is proposed.Theoretical conclusions and numerical evaluations show that the proposed estimator has higher efficiency than previous estimators.展开更多
Currently,working with partially observed functional data has attracted a greatly increasing attention,since there are many applications in which each functional curve may be observed only on a subset of a common doma...Currently,working with partially observed functional data has attracted a greatly increasing attention,since there are many applications in which each functional curve may be observed only on a subset of a common domain,and the incompleteness makes most existing methods for functional data analysis ineffective.In this paper,motivated by the appealing characteristics of conditional quantile regression,the authors consider the functional linear quantile regression,assuming the explanatory functions are observed partially on dense but discrete point grids of some random subintervals of the domain.A functional principal component analysis(FPCA)based estimator is proposed for the slope function,and the convergence rate of the estimator is investigated.In addition,the finite sample performance of the proposed estimator is evaluated through simulation studies and a real data application.展开更多
基金supported by the Natural Science Foundation of China under Grant Nos.11271014 and 11971045。
文摘This paper is focused on the goodness-of-fit test of the functional linear composite quantile regression model.A nonparametric test is proposed by using the orthogonality of the residual and its conditional expectation under the null model.The proposed test statistic has an asymptotic standard normal distribution under the null hypothesis,and tends to infinity in probability under the alternative hypothesis,which implies the consistency of the test.Furthermore,it is proved that the test statistic converges to a normal distribution with nonzero mean under a local alternative hypothesis.Extensive simulations are reported,and the results show that the proposed test has proper sizes and is sensitive to the considered model discrepancies.The proposed methods are also applied to two real datasets.
基金supported by the National Natural Science Foundation of China under Grant No.10971007Foundation of Academic Discipline Program at Central University of Finance and Economics+2 种基金Funding Project of Science and Technology Research Plan of Beijing Education Committee under Grant No.00600054K1002Fund of 211 Project at Central University of Finance and Economics2012 National Project of Statistical Research
文摘This paper considers the estimation of a semiparametric isotonic regression model when the covariates are measured with additive errors and the response is randomly right censored by a censoring time.The authors show that the proposed estimator of the regression parameter is rootn consistent and asymptotically normal.The authors also show that the isotonic estimator of the functional component,at a fixed point,is cubic root-n consistent and converges in distribution to the slope at zero of the greatest convex minorant of the sum of a two-sided standard Brownian motion and the square of the time parameter.A simulation study is carried out to investigate the performance of the estimators proposed in this article.
基金the National Nature Science Foundation of China under Grant Nos.11571024and 11771032the Humanities and Social Science Foundation of Ministry of Education of China under Grant No.20YJCZH245。
文摘Linear regression models for interval-valued data have been widely studied.Most literatures are to split an interval into two real numbers,i.e.,the left-and right-endpoints or the center and radius of this interval,and fit two separate real-valued or two dimension linear regression models.This paper is focused on the bias-corrected and heteroscedasticity-adjusted modeling by imposing order constraint to the endpoints of the response interval and weighted linear least squares with estimated covariance matrix,based on a generalized linear model for interval-valued data.A three step estimation method is proposed.Theoretical conclusions and numerical evaluations show that the proposed estimator has higher efficiency than previous estimators.
基金supported by the National Natural Science Foundation of China under Grant No.11771032。
文摘Currently,working with partially observed functional data has attracted a greatly increasing attention,since there are many applications in which each functional curve may be observed only on a subset of a common domain,and the incompleteness makes most existing methods for functional data analysis ineffective.In this paper,motivated by the appealing characteristics of conditional quantile regression,the authors consider the functional linear quantile regression,assuming the explanatory functions are observed partially on dense but discrete point grids of some random subintervals of the domain.A functional principal component analysis(FPCA)based estimator is proposed for the slope function,and the convergence rate of the estimator is investigated.In addition,the finite sample performance of the proposed estimator is evaluated through simulation studies and a real data application.
