Let Tn be the number of triangles in the random intersection graph G(n,m,p).When the mean of Tn is bounded,we obtain an upper bound on the total variation distance between Tn and a Poisson distribution.When the mean o...Let Tn be the number of triangles in the random intersection graph G(n,m,p).When the mean of Tn is bounded,we obtain an upper bound on the total variation distance between Tn and a Poisson distribution.When the mean of Tn tends to infinity,the Stein–Tikhomirov method is used to bound the error for the normal approximation of Tn with respect to the Kolmogorov metric.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
The authors establish the approximations to the distribution of M-estimates in a linear model by the bootstrap and the linear representation of bootstrap M-estimation, and prove that the approximation is valid in prob...The authors establish the approximations to the distribution of M-estimates in a linear model by the bootstrap and the linear representation of bootstrap M-estimation, and prove that the approximation is valid in probability 1. A simulation is made to show the effects of bootstrap approximation, randomly weighted approximation and normal approximation.展开更多
In this article, the general central limit theorem and Berry-Esseen bounds for finite-populationU-statistics with degree m are established under the very weak conditions, These resultssubstantially improve those of Zh...In this article, the general central limit theorem and Berry-Esseen bounds for finite-populationU-statistics with degree m are established under the very weak conditions, These resultssubstantially improve those of Zhao and Chen's (1987).展开更多
The dielectric breakdown（DB） model for a penny-shaped crack under a semipermeable boundary condition in a three-dimensional piezoelectric medium is studied.An approximate analytical solution is derived by using the ...The dielectric breakdown（DB） model for a penny-shaped crack under a semipermeable boundary condition in a three-dimensional piezoelectric medium is studied.An approximate analytical solution is derived by using the boundary integral equation with extended displacement discontinuity,and the corresponding boundary element method with double iterative approaches is developed to analyze the semi-permeable crack.The effect of electric boundary conditions on crack faces is discussed on the basis of DB model.By comparing the DB model with the polarization saturation（PS） model for different piezoelectric materials,some interesting phenomena related to the electric yielding zone and local J-integral are observed.展开更多
Weighted U-statistics and generalized L-statistics are commonly used in statistical inference and their asymptotic properties have been well developed.In this paper sharp non-uniform Berry–Esseen bounds for weighted ...Weighted U-statistics and generalized L-statistics are commonly used in statistical inference and their asymptotic properties have been well developed.In this paper sharp non-uniform Berry–Esseen bounds for weighted U-statistics and generalized L-statistic are established.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
文摘Let Tn be the number of triangles in the random intersection graph G(n,m,p).When the mean of Tn is bounded,we obtain an upper bound on the total variation distance between Tn and a Poisson distribution.When the mean of Tn tends to infinity,the Stein–Tikhomirov method is used to bound the error for the normal approximation of Tn with respect to the Kolmogorov metric.
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.
基金supported by Fund of 211 Program of SHUFEFund of Educational Committee of Shanghai
文摘The authors establish the approximations to the distribution of M-estimates in a linear model by the bootstrap and the linear representation of bootstrap M-estimation, and prove that the approximation is valid in probability 1. A simulation is made to show the effects of bootstrap approximation, randomly weighted approximation and normal approximation.
基金This work is also supported in part by the National Natural Science Foundation of China
文摘In this article, the general central limit theorem and Berry-Esseen bounds for finite-populationU-statistics with degree m are established under the very weak conditions, These resultssubstantially improve those of Zhao and Chen's (1987).
基金Project supported by the National Natural Science Foundation of China(Nos.11102186 and 11272290)the Science and Technology Key Project of Henan(No.132102210412)
文摘The dielectric breakdown（DB） model for a penny-shaped crack under a semipermeable boundary condition in a three-dimensional piezoelectric medium is studied.An approximate analytical solution is derived by using the boundary integral equation with extended displacement discontinuity,and the corresponding boundary element method with double iterative approaches is developed to analyze the semi-permeable crack.The effect of electric boundary conditions on crack faces is discussed on the basis of DB model.By comparing the DB model with the polarization saturation（PS） model for different piezoelectric materials,some interesting phenomena related to the electric yielding zone and local J-integral are observed.
基金The research of Q.-M.Shao is partly supported by Hong Kong RGC GRF 603710,2130344.
文摘Weighted U-statistics and generalized L-statistics are commonly used in statistical inference and their asymptotic properties have been well developed.In this paper sharp non-uniform Berry–Esseen bounds for weighted U-statistics and generalized L-statistic are established.
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.
