Consider heteroscedastic regression model Yni= g（xni） ＋ σniεni （1 〈 i 〈 n）, where σ2ni= f（uni）, the design points （xni, uni） are known and nonrandom, g（.） and f（.） are unknown functions defined on cl...Consider heteroscedastic regression model Yni= g（xni） ＋ σniεni （1 〈 i 〈 n）, where σ2ni= f（uni）, the design points （xni, uni） are known and nonrandom, g（.） and f（.） are unknown functions defined on closed interval [0, 1], and the random errors （εni, 1 ≤i≤ n） axe assumed to have the same distribution as （ξi, 1 ≤ i ≤ n）, which is a stationary and a-mixing time series with Eξi =0. Under appropriate conditions, we study asymptotic normality of wavelet estimators of g（.） and f（.）. Finite sample behavior of the estimators is investigated via simulations, too.展开更多
A partial linear model with missing response variables and error-prone covariates is considered. The imputation approach is developed to estimate the regression coefficients and the nonparametric function. The propose...A partial linear model with missing response variables and error-prone covariates is considered. The imputation approach is developed to estimate the regression coefficients and the nonparametric function. The proposed parametric estimators are shown to be asymptotically normal, and the estimators for the nonparametric part are proved to converge at an optimal rate. To construct confidence regions for the regression coefficients and the nonparametric function, respectively, the authors also propose the empirical-likelihood-based statistics and investigate the limit distributions of the empirical likelihood ratios. The simulation study is conducted to compare the finite sample behavior for the proposed estimators. An application to an AIDS dataset is illustrated.展开更多
This paper considers two estimators of θ= g（x） in a nonparametric regression model Y = g（x） ＋ ε（x∈ （0, 1）p） with missing responses： Imputation and inverse probability weighted esti- mators. Asymptotic nor...This paper considers two estimators of θ= g（x） in a nonparametric regression model Y = g（x） ＋ ε（x∈ （0, 1）p） with missing responses： Imputation and inverse probability weighted esti- mators. Asymptotic normality of the two estimators is established, which is used to construct normal approximation based confidence intervals on θ.展开更多
The Box-Cox transformation model has been widely used in applied econometrics, positive accounting, positive finance and statistics. There is a large literature on Box-Cox transformation model with linear structure. H...The Box-Cox transformation model has been widely used in applied econometrics, positive accounting, positive finance and statistics. There is a large literature on Box-Cox transformation model with linear structure. However, there is seldom seen on the discussion for such a model with partially linear structure. Considering the importance of the partially linear model, in this paper, a relatively simple semi-parametric estimation procedure is proposed for the Box-Cox transformation model without presuming the linear functional form and without specifying any parametric form of the disturbance, which largely reduces the risk of model misspecification. We show that the proposed estimator is consistent and asymptotically normally distributed. Its covariance matrix is also in a closed form, which can be easily estimated. Finally, a simulation study is conducted to see the finite sample performance of our estimator.展开更多
This paper studies the parameter estimation of multiple dimensional linear errors-in-variables (EV) models in the case where replicated observations are available in some experimental points. Asymptotic normality is e...This paper studies the parameter estimation of multiple dimensional linear errors-in-variables (EV) models in the case where replicated observations are available in some experimental points. Asymptotic normality is established under mild conditions, and the parameters entering the asymptotic variance are consistently estimated to render the result useable in the construction of large-sample confidence regions.展开更多
It is of great interest to estimate quantile residual lifetime in medical science and many other fields. In survival analysis, Kaplan-Meier（K-M） estimator has been widely used to estimate the survival distribution. ...It is of great interest to estimate quantile residual lifetime in medical science and many other fields. In survival analysis, Kaplan-Meier（K-M） estimator has been widely used to estimate the survival distribution. However, it is well-known that the K-M estimator is not continuous, thus it can not always be used to calculate quantile residual lifetime. In this paper, the authors propose a kernel smoothing method to give an estimator of quantile residual lifetime. By using modern empirical process techniques, the consistency and the asymptotic normality of the proposed estimator are provided neatly.The authors also present the empirical small sample performances of the estimator. Deficiency is introduced to compare the performance of the proposed estimator with the naive unsmoothed estimator of the quantile residaul lifetime. Further simulation studies indicate that the proposed estimator performs very well.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.10871146the Grant MTM2008-03129 from the Spanish Ministry of Science and Innovation
文摘Consider heteroscedastic regression model Yni= g（xni） ＋ σniεni （1 〈 i 〈 n）, where σ2ni= f（uni）, the design points （xni, uni） are known and nonrandom, g（.） and f（.） are unknown functions defined on closed interval [0, 1], and the random errors （εni, 1 ≤i≤ n） axe assumed to have the same distribution as （ξi, 1 ≤ i ≤ n）, which is a stationary and a-mixing time series with Eξi =0. Under appropriate conditions, we study asymptotic normality of wavelet estimators of g（.） and f（.）. Finite sample behavior of the estimators is investigated via simulations, too.
基金This research is supported by the National Social Science Foundation of China under Grant No. 11CTJ004, the National Natural Science Foundation of China under Grant Nos. 10871013 and 10871217, the National Natural Science Foundation of Beijing under Grant No. 1102008, the Research Foundation of Chongqing Municipal Education Commission under Grant Nos. KJ110720 and KJ100726, and the Natural Science Foundation of Guangxi under Grant No. 2010GXNSFB013051.
文摘A partial linear model with missing response variables and error-prone covariates is considered. The imputation approach is developed to estimate the regression coefficients and the nonparametric function. The proposed parametric estimators are shown to be asymptotically normal, and the estimators for the nonparametric part are proved to converge at an optimal rate. To construct confidence regions for the regression coefficients and the nonparametric function, respectively, the authors also propose the empirical-likelihood-based statistics and investigate the limit distributions of the empirical likelihood ratios. The simulation study is conducted to compare the finite sample behavior for the proposed estimators. An application to an AIDS dataset is illustrated.
基金This research is supported by he National Natural Science Foundation of China under Grant Nos. 10661003 and 10971038, and the Natural Science Foundation of Guangxi under Grant No. 2010GXNSFA013117.
文摘This paper considers two estimators of θ= g（x） in a nonparametric regression model Y = g（x） ＋ ε（x∈ （0, 1）p） with missing responses： Imputation and inverse probability weighted esti- mators. Asymptotic normality of the two estimators is established, which is used to construct normal approximation based confidence intervals on θ.
基金funded in part by National Natural Science Foundation of China (Grant No. 71032005)the MOE Project of Key Research Institute of Humanities and Social Science in University (Grant No. 10JJD630005)+3 种基金supported in part by New Century Excellent Talent Supporting program (Grant No. NCET-09-0538)National Natural Science Foundation of China(Grant Nos. 70871073 and 71171127)Shanghai Leading Academic Discipline Project (Grant No. B801)the Key Laboratory of Mathematical Economics (SUFE), Ministry of Education of China
文摘The Box-Cox transformation model has been widely used in applied econometrics, positive accounting, positive finance and statistics. There is a large literature on Box-Cox transformation model with linear structure. However, there is seldom seen on the discussion for such a model with partially linear structure. Considering the importance of the partially linear model, in this paper, a relatively simple semi-parametric estimation procedure is proposed for the Box-Cox transformation model without presuming the linear functional form and without specifying any parametric form of the disturbance, which largely reduces the risk of model misspecification. We show that the proposed estimator is consistent and asymptotically normally distributed. Its covariance matrix is also in a closed form, which can be easily estimated. Finally, a simulation study is conducted to see the finite sample performance of our estimator.
基金This project is supported by the National Natural Science Foundation of China (No.19631040)
文摘This paper studies the parameter estimation of multiple dimensional linear errors-in-variables (EV) models in the case where replicated observations are available in some experimental points. Asymptotic normality is established under mild conditions, and the parameters entering the asymptotic variance are consistently estimated to render the result useable in the construction of large-sample confidence regions.
基金supported by the National Natural Science Foundation of China under Grant No.71271128the State Key Program of National Natural Science Foundation of China under Grant No.71331006+4 种基金NCMISKey Laboratory of RCSDSCAS and IRTSHUFEPCSIRT(IRT13077)supported by Graduate Innovation Fund of Shanghai University of Finance and Economics under Grant No.CXJJ-2011-429
文摘It is of great interest to estimate quantile residual lifetime in medical science and many other fields. In survival analysis, Kaplan-Meier（K-M） estimator has been widely used to estimate the survival distribution. However, it is well-known that the K-M estimator is not continuous, thus it can not always be used to calculate quantile residual lifetime. In this paper, the authors propose a kernel smoothing method to give an estimator of quantile residual lifetime. By using modern empirical process techniques, the consistency and the asymptotic normality of the proposed estimator are provided neatly.The authors also present the empirical small sample performances of the estimator. Deficiency is introduced to compare the performance of the proposed estimator with the naive unsmoothed estimator of the quantile residaul lifetime. Further simulation studies indicate that the proposed estimator performs very well.
