条件密度双重核估计的强收敛速度

在适当的条件下,给出了条件密度双重核估计强收敛的速度。     

部分变量带误差的线性函数关系模型的参数估计及相合性

本文讨论了部分变量带误差的线性函数关系模型的参数估计问题，在较弱条件下证明了所获得的估计的强相合性，并给出了收敛速度。     

反周期函数的一种Hermite仿三角多项式插值逼近

杜金元等在2004年给出了Hermite仿三角多项式插值问题的基函数,且在插值函数具有一定解析性的条件下给出了余项公式。本文给出了反周期函数的一种Hermite仿三角多项式插值逼近,其对任意反周期连续函数都是收敛的。我们给出了收敛速度的一种估计。     

收敛因子法迭代求振动固有频率和振型

幂法迭代求前几阶固有频率和振型是振动算法之一。但当相邻两阶频率十分接近时,收敛速度大为降低。本文中探索了提高收敛速度的方法:类似于松弛法,在迭代中引进了收敛因子以减少计算次数。但本法中不采取将元素逐个松弛的做法,以免造成收敛因子值难以选取的困难。文中给出了选择收敛因子值的实用方法和收敛条件。最后在计算实例中对幂法和收敛因子法作了比较。     

一种强干扰下超弱水声信号自适应盲分离的快速算法

许多盲源分离算法对超弱信号收敛速度变慢甚至失效。文章提出一种算法 ,用FASTICA算法所得的分离矩阵作为一种基于输出去相关自适应盲分离算法的初始值 ,算法的收敛速度得到明显改善。算法的学习速率通过一种自适应算法选取 ,从而降低了算法收敛速度对学习步长的依赖。仿真结果表明 ,文中提出的算法对超弱信号特别有效 ,算法收敛速度大大增强。该算法可以用于分离强干扰下的弱水声信号     

一种拟Grünwald插值算子的加权L2收敛速度

证明了以第二类Tchebycheff多项式的零点为插值结点组的Grünwald插值算子列于L2下不是收敛算子列,后给出了一种于L2下收敛的拟Grünwald插值多项式,得到了基于加权L2下的收敛速度.     

钨合金棒材无模流变成形有限元分析

采用刚塑性有限元法分析钨合金棒材无模流变成形变形区速度场、应力场及变形力.收敛条件采用总能量泛函收敛准则、速度收敛准则、节点力不平衡量收敛准则的3个条件同时满足的收敛判定.给出钨合金棒材无模流变成形力能参数的数值解.变形力理论计算值与实验结果相吻合,相对误差小于10%.     

一些相依序列的强大数律和收敛速度

本文研究了正相协序列、负相协序列、强正相依序列以及鞅差序列的强极限性质.利用负相协序列和弱鞅序列的极大值矩不等式以及随机变量的截尾方法,得到了上述相依序列的强大数定律、强收敛速度以及相应的随机变量序列上确界的可积性.本文不仅将独立情形下的强大数定律推广到以上相依序列,并且还给出了其收敛速度.     

稳定的变步长自适应ⅡR陷波器及其在动目标检测中的应用

提出了一种变步长的自适应格型ⅡR陷波器算法,该算法在低信噪比条件下的收敛速度、跟踪速度与收敛精度方面比原变步长算法好,数值稳定性强.首次用两个级联的ⅡR陷波器实现了混响背景下的动目标检测,效果良好.     

一般正态序列极值的矩的收敛性

本文给出了一般正态随机变量序列极值的“规范化”的矩的收敛条件、结果及收敛速度,作为推论、还给出了m-相依,平稳正态序列极值的矩的相应收敛性结论。     

Estimation of the conditional distribution in a conditional Koziol-green model

We introduce a new estimator for the conditional distribution functions under the proportional hazards model of random censorship. Such estimator generalizes the one proposed by Abdushkurov, Chen and Lin when covariates are present. Asymptotic theory is given for this estimator. First, we established the strong consistency, and also obtain the rate of this convergence. Then, an asymptotic representation for the conditional distribution function estimator leads us to derive its asymptotic normality. The practical performance of the estimation procedure is illustrated on a real data set. Finally, as a further application of the new estimator, some functionals of interest in survival exploratory analysis are brieflys discussed. For the second author, this research was supported by a Human Capital postdoc fellowship, under the Programme ERB-CHRX-CT 940693.     

NA相依样本的非参数核估计

假设非参数衰退模型Yi=g(Xi)+iε,其中残差{iε}是一个具有未知公共密度函数f(x)的NA相依样本,g(x)=E(Y+X=x)是未知衰退函数.今首先在残差基础上定义了非参数估计gn(x)和^fn(x),并在适当条件下证明了gn(x)和^fn(x)分别是g(x)和f(x)的强一致相合估计,同时给出了相应的收敛速度.     

部分线性变量含误差的网格数据模型的估计

针对网格数据构建了部分线性变量含误差模型。在部分线性变量含误差的网格数据模型解释变量为固定设计的情形下,分别在单向维度观测样本容量趋于无穷和两个维度观测样本容量同时趋于无穷时对模型线性部分的未知参数、误差方差和非线性部分的未知函数进行了大样本统计推断研究。对模型线性部分未知参数和误差方差的改进的最小二乘估计量,在较弱的条件下推出估计量具有强相合性并得到收敛速度;对模型非线性部分未知函数的样条函数估计量,在一定的条件下证明了其具有强相合性并得到其收敛速度。在一定的正则条件下,分别对单向维度观测样本容量趋于无穷和两个维度观测样本容量同时趋于无穷的两种情形证明了模型线性部分未知参数和误差方差的估计量服从渐近正态分布,并对每种情形给出了渐近方差的表达式。     

关于NA相依变量加权和收敛性的注记

评注了NA相依变量加权和收敛性的相关定理，借用杨善朝的不等式，在比较简洁的条件下改善了已有结果，特别是不必要求同分布。作为应用，给出了NA相依样本回归函数的一个强相合估计。     

The large deviation results for the nonlinear regression model with dependent errors

In this paper, we investigate the least squares (LS) estimator of the nonlinear regression model based on the extended negatively dependent errors which are widely dependent structures. Under the general conditions, we establish some large deviation results for the LS estimator of the nonlinear regression parameter, which can be applied to obtain a weak uniform consistency and a complete convergence rate for this estimator. In addition, some examples and simulations are presented for illustration.     

Recursive local polynomial regression under dependence conditions

In the case of the random design nonparametric regression, one recursive local polynomial smoother is considered. Expressions for the bias and the variance matrix of the estimators of the regression function and its derivatives are obtained under dependence conditions (strongly mixing processes). The obtained Mean Squared Error is shown to be larger than those of the analogous nonrecursive regression estimators, although retaining the same convergence rate. The properties of strong consistency with convergence rates are established for the proposed estimators. Finally, in order to analyse the influence of both the sample size and the dependence in the behaviour of the proposed recursive estimator, a simulation study is performed. This work has been partially supported by DGES Grant PB98-0182-C02-01 and by the Xunta de Galicia Grant XUGA10501B97     

Closed form stiffness matrices and error estimators for plane hierarchic triangular elements

Closed form expressions for the stiffness matrix and a simple error estimator and error indicator are derived for plane straight sided triangular finite elements in elasticity problems. The calculation of the error estimator is performed on an element by element basis, and is found to be very accurate and efficient. In general, the solutions for benchmark problems using the error indicators for selective refinement of the regions show accelerated convergence when compared to the convergence rate of solutions using uniform mesh refinement. Evaluation of the stiffness matrices and error estimators using explicit formulations is found to be several times faster than numerical integration.     

Nonlinear Tikhonov regularization in Hilbert scales with balancing principle tuning parameter in statistical inverse problems

In this article, we study the balancing principle for Tikhonov regularization in Hilbert scales for deterministic and statistical nonlinear inverse problems. While the rates of convergence in deterministic setting is order optimal, they prove to be order optimal up to a logarithmic term in the stochastic framework. The two-step approach allows us to consider a data-driven algorithm in a general error model for which an exponential behaviour of the tail of the estimator chosen in the first step is valid. Finally, we compute the overall rate of convergence for a Hammerstein operator equation and for a parameter identification problem. Moreover, we illustrate these rates for the last application after we study some large sample properties of the local polynomial estimator in a general stochastic framework.     

Weiss-Hill estimator

In this paper the asymptotic distributional behaviour is derived for a new estimator for the extreme value index γ of distribution, which is a combination of two estimators proposed by Weiss and Hill (Weiss, 1971, and Hill, 1975). For |γ|>1/2, the estimator outperforms the Moment estimator (Dekkers and al., 1989). in the sense that it has a smaller asymptotic variance than the latter; moreover, for γ>1/2 (γ<0, resp.) the estimator behaves asymptoticaly like the Hillresp. Weiss—estimator; for |γ|<1/2 the estimator does not achieve the same rate of convergence as the Moment estimator. Simulation results concerning the comparison of the mentioned estimators are also presented. This research project was partially supported by FCT/PRAXIS XXI/FEDER and POCTI.     

Bandwidth selection in kernel density estimation for interval-grouped data

When interval-grouped data are available, the classical Parzen–Rosenblatt kernel density estimator has to be modified to get a computable and useful approach in this context. The new nonparametric grouped data estimator needs of the choice of a smoothing parameter. In this paper, two different bandwidth selectors for this estimator are analyzed. A plug-in bandwidth selector is proposed and its relative rate of convergence obtained. Additionally, a bootstrap algorithm to select the bandwidth in this framework is designed. This method is easy to implement and does not require Monte Carlo. Both proposals are compared through simulations in different scenarios. It is observed that when the sample size is medium or large and grouping is not heavy, both bandwidth selection methods have a similar and good performance. However, when the sample size is large and under heavy grouping scenarios, the bootstrap bandwidth selector leads to better results.