PA误差下回归函数小波估计的渐近性质（英文）

本文研究了回归函数小波估计的渐进性质的问题.利用概率不等式方法,获得了函数g(·)的小波估计量的r-阶矩相合,依概率收敛和强收敛以及渐进正态性的结果,所获的结果推广了其他混合相依下的相应结果.     

Bazilevič函数的对数系数

本文研究了Bazilevič函数类B_α（C,D）的对数系数.利用构造一个非负函数和对复变函数模的积分进行估计的方法,获得了B_α（C,D）的对数系数,推广了一些已有的相关结果.     

时变扩散模型中扩散系数的小波估计

本文构造了一种时变扩散系数的小波估计. 与文献中一维扩散系数的非参数估计问题相比, 放宽了对扩散系数的限制, 假定扩散系数为满足线 性增长条件的Lipschitz函数. 利用鞅的性质, 将扩散方程中的估计问题转化为非参数回归模型, 并 给出了估计量的 L^r 收敛速度. 在此基础上证明了估计量的强相合性. 利用强相合性, 可以在任何概率测度下用统一方法构造 的小波估计量来估计时变扩散系数.     

威布尔分布族刻度参数的经验Bayes检验函数的收敛速度

本文研究了在"加权线性损失"下,威布尔分布族刻度参数经验Bayes (EB)检验问题.利用概率密度函数的递归核估计,构造了刻度参数的经验Bayes检验函数,并获得了它的收敛速度,在适当的条件下,收敛速度的阶可任意接近O(n^-1),推广了文献的结果.最后给出一个有关本文主要结果的例子.     

P*(k)线性互补问题基于新核函数的大步校正算法

本文研究了P_*(k)线性互补问题的大步校正原始-对偶内点算法.基于一个强凸且不同于通常的对数函数和自正则函数的新核函数,对具有严格可行初始点的该问题,算法获得的迭代复杂性为O((1+2k)√n(log n)² log (n)/(ε),该结果缩小了大步校正内点算法的实际计算与理论复杂性界之间的差距.     

费马q-差分微分方程整函数解的增长性研究

本文研究了费马q-差分微分方程的整函数解的相关问题.利用经典和差分的Nevanlinna理论和函数方程理论的研究方法,获得了q-差分微分方程整函数解增长性的几个结果.     

具有高逼近阶和正则性的双向加细函数和双向小波

引入了双向加细函数和双向小波的概念,并研究双向加细方程 的分布解(或L²稳定解)的存在性, 其中整数m≥2. 基于正向面具{p_k⁺} 和 负向面具{p_k^-} , 建立了确保双向加细方程具有紧支撑分布解或L²稳定解所需要的条件. 更进一步地, 给出了双向加细方程的L²稳定解能产生一个MRA所需要的条件. 充分讨论了φ(x) 的支撑区间. 给出正交双向加细函数和双向小波的定义, 建立了双向加细函数的正交准则. 给出一类正交双向加细函数和正交双向小波 的构造算法. 另外,也给出了具有非负面具的、高逼近阶和正则性的双向加细函数的构造算法. 最后,构造了两个算例.     

由Dziok-Srivastava算子定义的多叶解析函数类的性质

本文研究了由Dziok-Srivastava算子H(a₁,…,a_q;b₁,…,b_s)定义的关于参数b_j ∈ C\Z₀^-(Z₀^-=0,-1,-2,…;j=1,2,…,s)的多叶解析函数类W_p(H(b_j+1);A,B).利用微分从属的方法和卷积的性质,获得了该类函数的特征性质和包含结果,推广了一些已知结果.     

Fp空间上相关的复合算子

本文研究了F_p空间上的复合算子的几个问题.应用泛函分析的方法研究了F_p(相应地,F_p,0)空间到Bloch空间的复合算子的有界性和紧性的若干充分和必要条件.此外,也刻画了当1 ≤ p < ∞时从Bloch空间到F_p空间的等距复合算子并且证明了当0 < p < ∞时F_p,0上的复合算子不具有Fredholm性.     

图的2-强边色数的上界

本文研究了图的2-强边色数的上界. 利用图染色的概率方法中的一般局部引理, 得到了3 ≤Δ ≤ 730时,χ''_s(G,2) ≤ 2Δ + 1, 推广了参考文献[11,12]中的结果     

Nonlinear wavelet density estimation with censored dependent data

In this paper, we provide an asymptotic expansion for the mean integrated squared error (MISE) of nonlinear wavelet estimator of survival density for a censorship model when the data exhibit some kind of dependence. It is assumed that the observations form a stationary and α‐mixing sequence. This asymptotic MISE expansion, when the density is only piecewise smooth, is same. However, for the kernel estimators, the MISE expansion fails if the additional smoothness assumption is absent. Also, we establish the asymptotic normality of the nonlinear wavelet estimator. Copyright © 2011 John Wiley & Sons, Ltd.     

Wavelet estimation in diffusions with periodicity

We consider a time-inhomogeneous diffusion process, whose drift term contains a deterministic T-periodic signal with known periodicity. This signal is supposed to be contained in a Besov space, we try to estimate it using a non-parametric wavelet estimator. Our estimator is inspired by the thresholded wavelet density estimator constructed by Donoho, Johnstone, Kerkyacharian and Picard in 1996. Under certain ergodicity assumptions to the process, we can give the same asymptotic rate of convergence as for the density estimator.     

Wavelet Estimator of Long-Range Dependent Processes

In this contribution, the statistical properties of the wavelet estimator of the long-range dependence parameter introduced in Abry et al. (1995) are discussed for a stationary Gaussian process. This contribution complements the heuristical discussion presented in Abry et al. (1999), by taking into account the correlation between the wavelet coefficients (which is discarded in the mentioned reference) and the bias due to the short-memory component. We derive expressions for the estimators asymptotic bias, variance and mean-squared error as functions of the scale used in the regression and some user-defined parameters. Consistency of the estimator is obtained as long as the scale index j _T goes to infinity and 2^j _T /T0, where T denotes the sample size. Under these and some additional conditions assumed in the paper, we also establish the asymptotic normality of this estimator.     

Berry-Esseen bounds for wavelet estimator in a regression model with linear process errors

In this paper, we derive the Berry-Esseen bounds of the wavelet estimator for a nonparametric regression model with linear process errors generated by φ-mixing sequences. As application, by the suitable choice of some constants, the convergence rate O(n^−1/6) of uniformly asymptotic normality of the wavelet estimator is obtained. Our results generalize some known results in the literature.     

Estimation of nonlinear autoregressive models using design-adapted wavelets

We estimate nonlinear autoregressive models using a design-adapted wavelet estimator. We show two properties of the wavelet transform adapted to an autoregressive design. First, in an asymptotic setup, we derive the order of the threshold that removes all the noise with a probability tending to one asymptotically. Second, with this threshold, we estimate the detail coefficients by soft-thresholding the empirical detail coefficients. We show an upper bound on thel ₂-risk of these soft-thresholded detail coefficients. Finally, we illustrate the behavior of this design-adapted wavelet estimator on simulated and real data sets. Financial support from the contract ‘Projet d'Actions de Recherche Concertées’ nr. 98/03-217 from the Belgian government, and from the IAP research network nr. P5/24 of the Belgian State (Federal Office for Scientific, Technical and Cultural Affairs) is gratefully acknowledged.     

Asymptotic normality of wavelet density estimator under censored dependent observations

In this paper, we discuss the asymptotic normality of the wavelet estimator of the density function based on censored data, when the survival and the censoring times form a stationary ??-mixing sequence. To simulate the distribution of estimator such that it is easy to perform statistical inference for the density function, a random weighted estimator of the density function is also constructed and investigated. Finite sample behavior of the estimator is investigated via simulations too.     

On Distribution of Error of Linear Wavelet Estimator of Probability Density

We establish the asymptotic normality of the squared L ²-norm of the approximation error of a linear wavelet estimator of the density of a distribution. The calculations are based on the smallness of correlations between the coefficients of the high-frequency part of the multiresolution expansion of the estimator.Supported by the FCT Foundation (Portugal) in the framework of the project Probability and Statistics (2000–2002), Centro de Matematica, Universidade da Beira Interior.__________Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 2, pp. 184–207, April–June, 2005.     

Nonlinear wavelet estimation of regression function with random desigm

The nonlinear wavelet estimator of regression function with random design is constructed. The optimal uniform convergence rate of the estimator in a ball of Besov spaceB ³ _p,q is proved under quite general assumpations. The adaptive nonlinear wavelet estimator with near-optimal convergence rate in a wide range of smoothness function classes is also constructed. The properties of the nonlinear wavelet estimator given for random design regression and only with bounded third order moment of the error can be compared with those of nonlinear wavelet estimator given in literature for equal-spaced fixed design regression with i.i.d. Gauss error. Project supported by Doctoral Programme Foundation, the National Natural Science Foundation of China (Grant No. 19871003) and Natural Science Fundation of Heilongjiang Province, China.     

Étude asymptotique locale de l'estimateur par ondelettesA law of the iterated logarithm for wavelet density estimator

We state a pointwise central limit theorem for the linear wavelet density estimator in a more general setting than the result of Wu [12]. Furthermore, we also give a pointwise law of the iterated logarithm for this density estimator. Our proof of the law of the iterated logarithm uses the results of Mason [9] on the asymptotic behavior of the tail empirical process. To cite this article: A. Massiani, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 553–556.     

Wavelet Threshold Estimation of a Regression Function with Random Design

The wavelet threshold estimator of a regression function for the random design is constructed. The optimal uniform convergence rate of the estimator in a ball of Besov Space B^s_p, q is proved under general assumptions. The adaptive wavelet threshold estimator with near-optimal convergence rate in a wide range of Besov scale is also constructed.