关于Devroye－Wagner核估计的一个注记

本文研究了Ｄｅｖｒｏｙｅ和Ｗａｇｎｅｒ提出的两个核估计的有偏性，并给出这两个核估计的Ｐａｒｚｅｎ－Ｒｏｓｅｎｂｌａｔｔ核估计有偏性的一个统一的证明．     

回归系数的综合岭估计

本文提出了回归系数的一种新的有偏估计－－综合岭估计，讨论了综合岭估计的优良性，可容许怀等性质，给出了其迭代和极小均方程误差的无偏估计解，在综合估计下，岭估计和根方估计作为其特例，从而统一了岭估计和根方估计理论。     

病态条件下的一个有偏估计

在线性回归问题中的病态条件下，提出了一个新的有偏估计及容许性证明.[1]中的估计实为此估计的一个特例.进一步针对两种特殊情况，给出了特殊的有偏估计及其容许性证明.     

有偏抽样下带终止时间和带信息观察时间的纵向数据分析

纵向数据经常出现在生物医学等实际领域,而且在许多情况下,观察时间和终止时间是带信息的,同时可能会存在有偏抽样.本文在有偏抽样下,对于带信息观察时间和终止时间的纵向数据,提出了一个联合建模方法,并利用借代力量方法给出了模型参数的估计,同时获得了这些估计的渐近性质.最后,提出一种模型检验方法.     

回归系数的stein型主成分估计

对于设计阵Ｘ呈病态的线性回归模型，本文提出了一种新的关于回归系数的有偏估计─ｓｔｅｉｎ型主成分估计，并在均方误差意义下，论证了在一定条件下ｓｔｅｉｎ型主成分估计优于主成分估计，因此也优于ｓｔｅｉｎ型ＯＬＳ估计与ＯＬＳ估计，最后，我们又对偏参数的存在性，最优性进行了讨论，并得出了一些重要结论．     

两水平无重复因析试验散度效应的估计

本文对两水平无重复因析试验给出了散度效应的一种新的估计,称为AMH估计,改进了文献中散度效应的较好的MH估计的一个缺陷,给出并证明了AMH估计的无偏条件,证明了AMH估计比MH估计有更小的方差下界.最后通过模拟试验比较了AMH和MH估计的偏度,方差和均方误差.     

广义比估计与广义差估计及其优良性

本文提出了一个新的估计-广义比估计，将它与通常的广义差估计作了比较，并讨论了这两种估计的优良性．最后给出了一个有意义的应用．     

半参数回归模型的一类压缩估计

研究了半参数回归模型的参数估计问题,利用压缩估计方法给出了模型的一类有偏估计,并与最小二乘估计、岭估计、几乎无偏岭估计进行了比较.在均方误差意义下,新的压缩估计明显优于最小二乘估计.最后讨论了有偏参数选取的问题.     

混合系数线性模型参数的广义Liu估计

本文研究连续测量数据情况下的混合系数线性模型的参数估计问题.利用压缩估计方法给出了该模型的一类新的有偏估计-广义Liu估计,并在均方误差意义下,证明此类估计分别优于最小二乘估计、Liu估计.最后讨论参数的选取问题.     

条件概率密度函数核估计的误差分析及其最优带宽的选择

本文在α-混合严平稳过程的假设下，研究了条件概率密度核估计的偏和均方误差．在此基础上给出了核估计的渐近最优带宽，并以S＆P500指数为例展示了本文的结果．     

复杂网络幂律度分布和层次聚集函数标度指数的一种新的估计方法

提出一种估计复杂网络幂律度分布和层次聚集函数标度指数的新方法,并给出求解这些指数的数值算法．该方法可以克服目前网络研究中采用的图形线性拟合估计方法存在的偏差和不准确等不足之处．此外,通过对10个CNN网络进行KS检验统计量的比较,证实该方法比图形方法具有更好的拟合效果．     

ESTIMATING A STOCHASTIC MODEL OF POPULATION DYNAMICS WITH AN APPLICATION TO KANGAROOS

In this study, we derive stochastic models of population dynamics and devise a new method of estimating the models. The models allow growth and harvest to be nonlinear functions of stochastic processes and the error terms to be nonlinear and heteroskedastic. Ordinary least-squares estimates would be biased and inefficient and generalized least-squares estimates cannot be calculated. Therefore, we implement nonlinear maximum likelihood methods to find unbiased and efficient estimates of parameters. The method is applied to the population dynamics of kangaroos in South Australia. Aerial survey data of kangaroo numbers are combined with harvest, effort and rainfall data to estimate the growth and harvest functions and the variances of the stochastic processes which drive the system. Results suggest that growth and harvest should be modeled as functions of stochastic processes and that observations on kangaroo numbers are critical for estimating population dynamics. The results also indicate that the estimation method works well and is a viable alternative to ARIMA and GARCH models, particularly for small data sets.     

Regularity of Viscosity Solutions of the Biased Infinity Laplacian Equation

In this paper, we are interested in the regularity estimates of the nonnegative viscosity super solution of the $β$−biased infinity Laplacian equation $$∆^β_∞u = 0,$$ where $β ∈ \mathbb{R}$ is a fixed constant and $∆^β_∞u := ∆^N_∞u + β|Du|,$ which arises from the random game named biased tug-of-war. By studying directly the $β$−biased infinity Laplacian equation, we construct the appropriate exponential cones as barrier functions to establish a key estimate. Based on this estimate, we obtain the Harnack inequality, Hopf boundary point lemma, Lipschitz estimate and the Liouville property etc.     

Estimating the bias on the logdeterminant transformation for evolutionary trees

The logarithm of the determinant of a contingency table allows evolutionary information to be recovered from data generated under very general stochastic models. The variance of the estimate of the dissimilarity between taxa is generally estimated with the help of resampling methods. We show that this technique leads to biased estimates, and we derive exact formula. Practical implications are considered.     

Smoothing Methods for Nonlinear Complementarity Problems

In this paper, we present some new smoothing techniques to solve general nonlinear complementarity problems. Under a weaker condition than monotonicity as on the original problems, we prove convergence of our methods. We also present an error estimate under a general monotonicity condition. Some numerical tests confirm the efficiency of the proposed methods.     

基于泛岭估计对岭估计过度压缩的改进方法

岭估计是解决多元线性回归多重共线性问题的有效方法,是有偏的压缩估计。与普通最小二乘估计相比,岭估计可以降低参数估计的均方误差,但是却增大残差平方和,拟合效果变差。本文提出一种基于泛岭估计对岭估计过度压缩的改进方法,可以改进岭估计的拟合效果,减小岭估计残差平方和的增加幅度。     

线性回归诊断的若干问题

本文对于线性回归诊断提出了几种新的模型和方法。我们首次研究了方差加权和均值漂移的混合模型,得到了相应的诊断统计量。本文还引入了罚函数方法,并以此为工具,讨论了若干有偏估计的影响度量,最后,本文提出了基于重心的诊断统计量,对于识别异常点有较好的效果。     

Multistart method with estimation scheme for global satisfycing problems

We present a multistart method for solving global satisfycing problems. The method uses data generated by linearly converging local algorithms to estimate the cost value at the local minimum to which the local search is converging. When the estimate indicates that the local search is converging to a value higher than the satisfycing value, the local search is interrupted and a new local search is initiated from a randomly generated point. When the satisfycing problem is difficult and the estimation scheme is fairly accurate, the new method is superior over a straightforward adaptation of classical multistart methods.