一个有效估计:半参数非时齐扩散模型的局部线性复合分位回归估计

主要研究半参数非时齐扩散模型的参数估计问题.基于非时齐扩散模型的离散观测样本,首先得到漂移参数的局部线性复合分位回归估计,并证明估计量的渐近偏差、渐近方差和渐近正态性.其次,讨论了带宽的选择和局部线性复合分位回归估计关于局部线性最小二乘估计的渐近相对效,所得到的局部估计较局部线性最小二乘估计更为有效.最后,通过模拟说明了局部线性复合分位回归估计比局部线性最小二乘估计的模拟效果更好.     

Statistical analysis of two-parameter generalized Birnbaum-Saunders Cauchy distribution

The image features of density function and failure rate function are studied in detail for two-parameter generalized Birnbaum-Saunders Cauchy fatigue life distribution. The logarithmic moment estimation and other two point estimations of parameters are proposed under full sample, and the precisions of point estimations are investigated by Monte-Carlo simulations. The approximate interval estimations of parameters are given by using Taylor expansion, and the precisions of approximate interval estimations are investigated by Monte-Carlo simulations. Finally, several examples show the feasibility of the methods.     

Fehlerabsehätzung beim verfahren von wolfe zur lösung quadratischer optimierungsproblem mit hilfe der intervallarithmetik

This paper is dealt with error estimations for solutions of quadratic programming problems. These estimations are given by solution of a linear system of equations by means of the methods of interval arithmetic. Therefore it is quite certain that the round off errors are also included in these estimations.     

Local Linear Estimations of Time-Varying Parameters for Time-Inhomogeneous Diffusion Models

This paper studies the local linear estimations of the time-varying parameters for time-inhomogeneous diffusion models. Based on discretely observed sample of time-inhomogeneous diffusion models, the local linear estimations of the drift parameters are proposed and their standard errors are discussed. Considering the volatility parameter being positive, we obtain the kernel weighted estimation of the diffusion parameter by using locally log-linear fitting, and discuss asymptotic bias, asymptotic variance and asymptotic normal distribution of volatility function. It is shown that the local estimations proposed perform well through simulation studies.     

并联压力—强度模型可靠性研究

In this paper,the reliability of a parallel stress-strength model of exponentiated Pareto distribution is discussed.Different point estimations and interval estimations are proposed.The point estimators obtained are maximum likelihood and Bayesian estimators.The interval estimations obtained are approximate,exact,bootstrap-p and bootstrap-t confidence intervals and Bayesian credible interval.Different methods and the corresponding confidence intervals are demonstrated using some simulation studies.     

基于截尾数据指数Pareto分布应力-强度模型的可靠性

在II型双截尾删失计划下，讨论了当系统被独立的随机施加指数Pareto （EP）压力时的系统可靠性问题.作者给出了系统可靠性参数的不同点估计和区间估计，其中点估计包括一致最小方差无偏估计（UMVUE）和最大似然估计（MLE）；区间估计包括精确置信区间，近似置信区间和bootstrap的区间估计.为了评价不同估计方法效果，作者提供数值模拟结果；最后提供了一个真实数据的分析结果来演示本文提出的方法.     

有缺失数据的2×2×2列联表的参数估计

本文讨论了缺失数据的 2× 2× 2列联表的参数估计问题 ,通过给出适当的模型和观测数据模式 ,我们给出了各列联表各细胞参数的估计 ,并且证明这些估计是G -Markov的     

Mixed Estimations and Bayes Estimation of theRegression Coefficient in Multivariate Linear Model

ＭｉｘｅｄＥｓｔｉｍａｔｉｏｎｓａｎｄＢａｙｅｓＥｓｔｉｍａｔｉｏｎｏｆｔｈｅＲｅｇｒｅｓｓｉｏｎＣｏｅｆｆｉｃｉｅｎｔｉｎＭｕｌｔｉｖａｒｉａｔｅＬｉｎｅａｒＭｏｄｅｌ￥ＨｕａｎｇＹａｎｇｘｉｎ（黄养新）（ＷｕｈａｎＵｎｉｖｅｒｓｉｔｙｏｆＴｅｃｈ...     

Approximation in eigenvalue problems for holomorphic fredholm operator functions I

The approximation of a holomorphic eigenvalue problem is considered. The main purpose is to present a construction by which the derivation of the asymptotic error estimations for the approximate eigenvalues of Fredholm operator functions can be reduced to the derivation of these estimations for the case of matrix functions. (Some estimations for the latter problem can be derived, in one's turn, from the error estimations for the zeros of the corresponding determinants.) The asymptotic error estimations are considered in part II of this paper, in [10]. By the presented construction also the stability of the algebraic multiplicity of eigenvalues by regular approximation is proved in Section 3

The presented construction, in essence, reproduces the constructions in [7] for the case of the compact approximation in subspaces and in [9] for the case of projection—like methods. It is simpler to use than similiar construction in [8], and allows unified consideration of the general case and the case of projection—like methods, what in [8, 9] was not achieved     

具部分缺失数据的两个柏松总体的估计和检验

本文讨论部分缺失数据两柏松分布总体的参数估计和总体相同的似然比检验,证明了估计的强相合性和渐近正态性,给出了似然比检验的极限分布,并讨论了基于精确分布的检验问题.     

Numerical Solution of the Reaction-Diffusion Equation

In this paper, we consider the numerical solution for the reaction-diffusion equation. A finite difference scheme and the basic error equality are given. Then the error estimations are proved for the periodic problem with $v(x,t)\geq 0$, the first and second boundary value problems with $v(x,t)\geq v_0＞0$, and for $v(U)\geq v_0›0$. Under some conditions such estimations imply the stabilities and convergences of the schemes.     

局部平稳短期利率扩散模型的半参数估计

主要研究局部平稳扩散模型的半参数估计．首先,基于局部常数拟合,利用局部加权最小二乘法得到了漂移参数函数的估计量．同时,通过Kolmogorov向前方程,得到了扩散函数的估计量．然后,分别讨论了所得估计量的相合性和渐近正态性．最后,通过模拟研究说明了估计量的有效性．     

分布函数的非参数最小二乘估计

By using the non-parametric least square method, the strong consistent estimations of distribution function and failure function are established, where the distribution function F(x)after logist transformation is assumed to be approximated by a polynomial. The performance of simulation shows that the estimations are highly satisfactory.     

Statistical Analysis Technique of Two-parameter Generalized Exponential Sum Distribution

A new life distribution is proposed, known as ``two-parameter generalized exponential sum distribution". We study the density function and failure rate function, the average failure rate function, the image features and the numerical characteristics of the mean residual life of the distribution. Several methods of calculating point estimation of parameters are discussed. Through the Monte-Carlo simulation, we compare the precision of the point estimations. In our opinion, the best linear unbiased estimation is the most optimal solution of these methods. At the same time, several methods of calculating parameters of interval estimations are given. We also discuss the precision of interval estimations by Monte-Carlo simulation and use the best linear unbiased estimation and the best linear invariant estimation to construct interval estimations which are better than other estimation method. Finally, several simulation examples and a case of maintaining tanks is used to illustrate the application of the methods presented in this paper.     

系数为梯形模糊数的模糊回归分析的最小二乘法

由于模糊数往往可以用梯形模糊数来逼近,因此对梯形模糊数的模糊回归模型的研究就有一定的实用价值.采用最小二乘的方法,针对输入为精确数、输出和回归系数都是梯形模糊数的模糊线性回归模型,讨论了该模型回归系数的最小二乘估计及误差项的估计,实例说明了提出的参数估计的拟合度比较好.     

On Approximation by Neural Networks with Optimized Activation Functions and Fixed Weights

Recently, Li [16] introduced three kinds of single-hidden layer feed-forward neural networks with optimized piecewise linear activation functions and fixed weights, and obtained the upper and lower bound estimations on the approximation accuracy of the FNNs, for continuous function defined on bounded intervals. In the present paper, we point out that there are some errors both in the definitions of the FNNs and in the proof of the upper estimations in [16]. By using new methods, we also give right approximation rate estimations of the approximation by Li’s neural networks.     

定数截尾两参数指数——威布尔分布形状参数的Bayes估计

在不同的损失函数下,本文研究了两参数指数—威布尔分布(EWD)形状参数的Bayes估计问题.基于定数截尾试验,当其中一个形状参数α已知时,给出了另一个形状参数θ在三种不同损失函数下的Bayes估计表达式,并求得了可靠度函数的Bayes点估计.最后运用随机模拟方法,将Bayes估计和极大似然估计进行了比较.结果表明,LINEX损失下Bayes估计的精度比极大似然估计高.     

IIRCT下泊松分布参数多变点模型的贝叶斯估计

通过添加缺损的寿命变量数据得到了带有不完全信息随机截尾试验下泊松分布参数多变点模型的完全数据似然函数,研究了变点位置参数和其它参数的满条件分布.利用Gibbs抽样与Metropolis-Hastings算法相结合的MCMC方法对各参数的满条件分布分别进行了抽样,把Gibbs样本的均值作为各参数的贝叶斯估计,并且详细介绍了MCMC方法的实施步骤.最后进行了随机模拟试验,试验结果表明各参数贝叶斯估计的精度都较高.     

二维RLW方程的Cauchy问题

通过椭圆积分求出了二维RLW方程椭圆余弦波解,并用先验估计方法证明了该方程Cauchy问题关于小x、y周期解的若干性质和解的唯一性、稳定性。     

Two-weighted estimations for the Hardy-Littlewood maximal function in ideal Banach spaces

We give conditions on a couple of ideal Banach spaces with weights which are both necessary and sufficient for the Hardy-Littlewood maximal function to satisfy the two-weighted estimations of weak type, and we consider a modification of the Hardy-Littlewood maximal function. We also give some conditions on weights in order for the Hardy-Littlewood maximal function and the modification under consideration to fulfil the two-weighted estimations of strong type.