Let (Ω, A, P) be a probability space, X(t, ω) a random function continuous in probability for t∈[0,+∞) or (-∞,+∞)(ω∈Ω), and F(t) a positive function continuous for t∈[0,+∞) or (-∞, +∞). If X(t, ω) and F(...Let (Ω, A, P) be a probability space, X(t, ω) a random function continuous in probability for t∈[0,+∞) or (-∞,+∞)(ω∈Ω), and F(t) a positive function continuous for t∈[0,+∞) or (-∞, +∞). If X(t, ω) and F(t) verify certain conditions, then there exists a sequence {Qn(t,ω)} of random polynomials such that we have almost surely: for t∈[0,+∞) or (-∞, +∞), lim|X(t, ω)-Qn(t, ω)|/F(t)=0.展开更多
We consider Jackson inequality in L^2 （B^d×T, Wκ,μ^B （x））, where the weight function Wκ,μ^B （X） is defined on the ball B^d and related to reflection group, and obtain the sharp Jackson inequalityEn-1,m-...We consider Jackson inequality in L^2 （B^d×T, Wκ,μ^B （x））, where the weight function Wκ,μ^B （X） is defined on the ball B^d and related to reflection group, and obtain the sharp Jackson inequalityEn-1,m-1（f）2≤κn,m（τ,r）ωr（f,t）2,τ≥2τn,λ,where Tn,λ is the first positive zero of the Gegenbauer cosine polynomial Cn^λ （cos θ）（n ∈ N）.展开更多
In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to...In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to construct the confidence interval of f(y|x) .展开更多
In this note, the random weighting approximations for empirical process indexed by abounded class of functions are obtained, and the strong uniform convergence rates of ran-dom weighting empirical processes are given....In this note, the random weighting approximations for empirical process indexed by abounded class of functions are obtained, and the strong uniform convergence rates of ran-dom weighting empirical processes are given. When unknown multivariate underlingdistributions are not confined by any additional condition, we obtain the random weightingapproximations for multivariate Von Mises statistics and their projection pursuits (PP). Thisresult is also true for the bootstrap approximation of empirical processes.展开更多
文摘Let (Ω, A, P) be a probability space, X(t, ω) a random function continuous in probability for t∈[0,+∞) or (-∞,+∞)(ω∈Ω), and F(t) a positive function continuous for t∈[0,+∞) or (-∞, +∞). If X(t, ω) and F(t) verify certain conditions, then there exists a sequence {Qn(t,ω)} of random polynomials such that we have almost surely: for t∈[0,+∞) or (-∞, +∞), lim|X(t, ω)-Qn(t, ω)|/F(t)=0.
基金supported by National Natural Science Foundation of China(11071019)Beijing Natural Science Foundation(1132001)
文摘We consider Jackson inequality in L^2 （B^d×T, Wκ,μ^B （x））, where the weight function Wκ,μ^B （X） is defined on the ball B^d and related to reflection group, and obtain the sharp Jackson inequalityEn-1,m-1（f）2≤κn,m（τ,r）ωr（f,t）2,τ≥2τn,λ,where Tn,λ is the first positive zero of the Gegenbauer cosine polynomial Cn^λ （cos θ）（n ∈ N）.
基金Supported by Natural Science Foundation of Beijing City and National Natural Science Foundation ofChina(2 2 30 4 1 0 0 1 30 1
文摘In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to construct the confidence interval of f(y|x) .
基金Project supported by the National Natural Science Foundation of China.
文摘In this note, the random weighting approximations for empirical process indexed by abounded class of functions are obtained, and the strong uniform convergence rates of ran-dom weighting empirical processes are given. When unknown multivariate underlingdistributions are not confined by any additional condition, we obtain the random weightingapproximations for multivariate Von Mises statistics and their projection pursuits (PP). Thisresult is also true for the bootstrap approximation of empirical processes.
