The inference for the parameters in a semiparametric regression model is studied by using the wavelet and the bootstrap methods. The bootstrap statistics are constructed by using Efron＇s resampling technique, and the...The inference for the parameters in a semiparametric regression model is studied by using the wavelet and the bootstrap methods. The bootstrap statistics are constructed by using Efron＇s resampling technique, and the strong uniform convergence of the bootstrap approximation is proved. Our results can be used to construct the large sample confidence intervals for the parameters of interest. A simulation study is conducted to evaluate the finite-sample performance of the bootstrap method and to compare it with the normal approximation-based method.展开更多
Point-wise confidence intervals for a nonparametric regression function with random design points are considered. The confidence intervals are those based on the traditional normal approximation and the empirical like...Point-wise confidence intervals for a nonparametric regression function with random design points are considered. The confidence intervals are those based on the traditional normal approximation and the empirical likelihood. Their coverage accuracy is assessed by developing the Edgeworth expansions for the coverage probabilities. It is shown that the empirical likelihood confidence intervals are Bartlett correctable.展开更多
Consider the model (1.6), where eij (j=1,…,Ni, i=1,2,…) are i.i.d.with mean 0 andwriance 1.Introduce a randomly weighted estimate βn defined by (1.8).Assuming e11 ～N(0, 1)and,the paper gives a necessary and suffic...Consider the model (1.6), where eij (j=1,…,Ni, i=1,2,…) are i.i.d.with mean 0 andwriance 1.Introduce a randomly weighted estimate βn defined by (1.8).Assuming e11 ～N(0, 1)and,the paper gives a necessary and sufficient condition for βn to be a consistent estimateof β0,and under some further restrictions a normal approximation fo βn is established whichcan be used in constructing a large sample confidence interval of β0. Finally, in the non-normalcase a theorem about the consistency of βn is proved.展开更多
The aim of the paper is to estimate the density functions or distribution functions measured by Wasserstein metric, a typical kind of statistical distances, which is usually required in the statistical learning. Based...The aim of the paper is to estimate the density functions or distribution functions measured by Wasserstein metric, a typical kind of statistical distances, which is usually required in the statistical learning. Based on the classical Bernstein approximation, a scheme is presented. To get the error estimates of the scheme, the problem turns to estimating the L1 norm of the Bernstein approximation for monotone C-1 functions, which was rarely discussed in the classical approximation theory. Finally, we get a probability estimate by the statistical distance.展开更多
基金Supported by National Natural Science Foundation of China (Grant Nos. 10571008, 10871013)Beijing Natural Science Foundation (Grant No. 1072004)Ph.D. Program Foundation of Ministry of Education of China (Grant No. 20070005003)
文摘The inference for the parameters in a semiparametric regression model is studied by using the wavelet and the bootstrap methods. The bootstrap statistics are constructed by using Efron＇s resampling technique, and the strong uniform convergence of the bootstrap approximation is proved. Our results can be used to construct the large sample confidence intervals for the parameters of interest. A simulation study is conducted to evaluate the finite-sample performance of the bootstrap method and to compare it with the normal approximation-based method.
文摘Point-wise confidence intervals for a nonparametric regression function with random design points are considered. The confidence intervals are those based on the traditional normal approximation and the empirical likelihood. Their coverage accuracy is assessed by developing the Edgeworth expansions for the coverage probabilities. It is shown that the empirical likelihood confidence intervals are Bartlett correctable.
文摘Consider the model (1.6), where eij (j=1,…,Ni, i=1,2,…) are i.i.d.with mean 0 andwriance 1.Introduce a randomly weighted estimate βn defined by (1.8).Assuming e11 ～N(0, 1)and,the paper gives a necessary and sufficient condition for βn to be a consistent estimateof β0,and under some further restrictions a normal approximation fo βn is established whichcan be used in constructing a large sample confidence interval of β0. Finally, in the non-normalcase a theorem about the consistency of βn is proved.
基金Supported by 973-Project of China(2006cb303102)the National Science Foundation of China(11461161006,11201079)
文摘The aim of the paper is to estimate the density functions or distribution functions measured by Wasserstein metric, a typical kind of statistical distances, which is usually required in the statistical learning. Based on the classical Bernstein approximation, a scheme is presented. To get the error estimates of the scheme, the problem turns to estimating the L1 norm of the Bernstein approximation for monotone C-1 functions, which was rarely discussed in the classical approximation theory. Finally, we get a probability estimate by the statistical distance.
