This paper studies the parameter estimation of one dimensional linear errors-in-variables(EV) models in the case that replicated observations are available in some experimental points.Asymptotic normality is establis...This paper studies the parameter estimation of one dimensional linear errors-in-variables(EV) models in the case that 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 construction of large-sample confidence regions.展开更多
Consider the following heteroscedastic semiparametric regression model：where {Xi, 1 〈 i 〈 n} are random design points, errors {ei, 1 〈 i 〈 n} are negatively associated （NA） random variables, （r2 = h（ui）, and...Consider the following heteroscedastic semiparametric regression model：where {Xi, 1 〈 i 〈 n} are random design points, errors {ei, 1 〈 i 〈 n} are negatively associated （NA） random variables, （r2 = h（ui）, and {ui} and {ti} are two nonrandom sequences on [0, 1]. Some wavelet estimators of the parametric component β, the non- parametric component g（t） and the variance function h（u） are given. Under some general conditions, the strong convergence rate of these wavelet estimators is O（n- 1 log n）. Hence our results are extensions of those re, sults on independent random error settings.展开更多
One important model in handling the multivariate data is the varying-coefficient partially linear regression model. In this paper, the generalized likelihood ratio test is developed to test whether its coefficient fun...One important model in handling the multivariate data is the varying-coefficient partially linear regression model. In this paper, the generalized likelihood ratio test is developed to test whether its coefficient functions are varying or not. It is showed that the normalized proposed test follows asymptotically x2-distribution and the Wilks phenomenon under the null hypothesis, and its asymptotic power achieves the optimal rate of the convergence for the nonparametric hypotheses testing. Some simulation studies illustrate that the test works well.展开更多
基金supported by the Doctoral Fund of Ludong University(LY2013001,LY201222)Science and Technology Development Projects of Shandong Province(2012YD01056)+2 种基金Shangdong Province Young and Middle-Aged Scientists Research Awards Fund(BS2013SF029)National Natural Science Foundation of China-Tianyuan Fund for Mathematics(11426126)Natural Science Foundation of Shandong Province(ZR2014AP007)
基金Project supported by the National Natural Science Foundation of China (No. 19631040).
文摘This paper studies the parameter estimation of one dimensional linear errors-in-variables(EV) models in the case that 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 construction of large-sample confidence regions.
基金supported by the National Natural Science Foundation of China (No. 11071022)the Key Project of the Ministry of Education of China (No. 209078)the Youth Project of Hubei Provincial Department of Education of China (No. Q20122202)
文摘Consider the following heteroscedastic semiparametric regression model：where {Xi, 1 〈 i 〈 n} are random design points, errors {ei, 1 〈 i 〈 n} are negatively associated （NA） random variables, （r2 = h（ui）, and {ui} and {ti} are two nonrandom sequences on [0, 1]. Some wavelet estimators of the parametric component β, the non- parametric component g（t） and the variance function h（u） are given. Under some general conditions, the strong convergence rate of these wavelet estimators is O（n- 1 log n）. Hence our results are extensions of those re, sults on independent random error settings.
基金supported by National Natural Science Foundation of China under Grant No.1117112the Fund of Shanxi Datong University under Grant No.2010K4+1 种基金the Doctoral Fund of Ministry of Education of China under Grant No.20090076110001National Statistical Science Research Major Program of China under Grant No.2011LZ051
文摘One important model in handling the multivariate data is the varying-coefficient partially linear regression model. In this paper, the generalized likelihood ratio test is developed to test whether its coefficient functions are varying or not. It is showed that the normalized proposed test follows asymptotically x2-distribution and the Wilks phenomenon under the null hypothesis, and its asymptotic power achieves the optimal rate of the convergence for the nonparametric hypotheses testing. Some simulation studies illustrate that the test works well.
