空间半参数变系数部分线性回归中的分位数估计

本文研究了空间数据变系数部分线性回归中的分位数估计. 模型中的参数估计量通过未知系数函数的分段多项式逼近得到, 而未知系数函数的估计量通过将参数估计量代入模型中并通过局部线性逼近得到. 文中推导了未知参数向量估计量的渐近分布, 并建立了未知系数函数估计量在内点及边界点的渐近分布. 通过Monte Carlo 模拟研究了估计量的有限样本性质.     

系数函数光滑度互不相同的变系数模型的一步估计法

该文提出了一种一步估计方法用以估计变系数模型中具有互不相同光滑度的未知函数, 所有未知函数和它们的导数的估计量由 一次极小化得到. 给出了估计量的渐近性质, 包括渐近偏差、方差和渐近分布, 一步估计量被证明达到了最优收敛速度.     

基于部分线性变系数空间误差模型的网络结构缺失数据借补估计

文章采用空间误差模型刻画个体之间的网络结构关系,讨论响应变量随机缺失时部分线性变系数空间误差模型的估计和借补问题.首先,利用矩阵分块和截面似然技术构建了参数估计量,并证明了参数估计量的渐近分布和未知系数函数估计量的收敛速度.其次基于部分线性变系数模型,提出了带有空间网络结构的缺失数据的借补方法.最后,通过蒙特卡洛模拟研究了估计量的有限样本性质,并将该方法应用于QQ数据集分析.     

随机截尾下污染数据部分线性模型的强相合估计

考虑一类新的污染数据部分线性模型,当受污染后的因变量被随机右截断时,就截断分布已知的情形,利用所获得截断观测数据构造了模型中的参数分量,非参数分量及污染系数的估计量,并在适当的条件下,证明了这些估计量的强相合性.     

基于众数回归的变系数部分非线性模型的稳健估计

针对变系数部分非线性模型,提出了一种稳健的基于众数回归的两阶段估计方法.首先,基于B-样条函数近似系数函数,利用QR正交分解技术构造了非线性模型,得到了参数的非线性最小二乘估计.其次,提出了变系数函数的众数回归估计量.在一定条件下,证明了估计量的渐近性质.通过数值模拟和实际数据分析,说明了所提估计方法的有效性.     

变系数模型中的逐元估计法

提出了一种叫做逐元估计法的方法用来估计变系数模型中的未知函数和它们的导数,构造了一种快速选择估计量窗宽和快速计算大量估计点的方法,推导了估计量的渐近正态性.通过Monte Carlo模拟研究了估计量的有限样本性质.     

变系数联立模型的局部线性广义矩变窗宽估计

在随机设计条件下,提出了一类变系数联立模型,运用局部线性广义矩变窗宽估计,对模型的变系数进行了估计,研究了估计量的大样本性质.利用概率论中大数定律和中心极限定理,证明了估计量的大样本性质,局部线性广义矩变窗宽估计具有相合性和渐进正态性.     

空间数据变系数回归中的B-spline估计法

本文借助B—spline函数逼近开发了一种整体估计程序,用以估计变系数回归中的未知系数函数．在较弱假设条件下,建立了未知函数B—spline估计量的整体收敛速度,渐近性结果显示B-spline估计量达到了最优收敛速度,并推导了未知函数B—spline估计量的渐近分布．本文还给出了一种光滑参数选择方法,通过Monte Carlo模拟研究了估计量的有限样本性质,并用文中提出的方法分析了1980年美国总统选举投票数据．     

关于洛伦兹曲线和基尼系数的统计推断

本文对于洛伦兹曲线的最一般定义,在无任何附加限制条件下,论证了基于样本数据所得到的洛仑兹曲线的通常估计量具有强相合性.在此基础上,证明了基尼系数和Schutz系数的通常估计量均具有强相合性.此外,导出了基尼系数估计量的渐进分布,并在此基础上给出了大样本情形下基尼系数的置信区间.     

完备的随机波动率模型的统计推断

完备的随机波动率模型是David G.Hobson and Rogers L G 于1998年引入一类新的随机波动率模型,与现有波动率模型相比,它有很多优点.本文讨论了这类模型的估计问题。通过测度变换,将系数σ(·)的估计转化为—般回归函数的估计问题,给出了该系数的核估计量,并证明了所得估计量的均方收敛性。     

导弹命中率的估计和检验

本文讨论了导弹可靠性试验中提出的有关命中率的估计和检验问题，考虑估计量Ｐ与命中率Ｐ的误差，它服从正态分布Ｎ（０，σ２Ｐ）。我们设法将非线性函数化为线性函数，运用线性函数的误差传递公式，设法得到σ２Ｐ的估计，从而可求得Ｐ的置信水平为１—α的区间估计。并由试验结果对命中率是否达到指标值作假设检验。     

Stopping rules,permutation invariance and sufficiency principle

In the context of sequential (point as well as interval) estimation, a general formulation of permutation-invariant stopping rules is considered. These stopping rules lead to savings in the ASN at the cost of some elevation of the associated risk—a phenomenon which may be attributed to the violation of the sufficiency principle. For the (point and interval) sequential estimation of the mean of a normal distribution, it is shown that such permutation-invariant stopping rules may lead to a substantial saving in the ASN with only a small increase in the associated risk.Work partially supported by (i) Office of Naval Research, Contract Number N00014-85-K-0548, and (ii) Office of Naval Research, Contract Number N00014-83-K-0387.     

Minimax estimation and the least squares method

This paper is devoted to the problem of minimax estimation of parameters in linear regression models with uncertain second order statistics. The solution to the problem is shown to be the least squares estimator corresponding to the least favourable matrix of the second moments. This allows us to construct a new algorithm for minimax estimation closely connected with the least squares method. As an example, we consider the problem of polynomial regression introduced by A. N. Kolmogorov     

三维空间形式中常平均曲率曲面的稳定性

本文利用共形度量高斯曲率的估计研究了三维空间形式N^3(C）中具常平均曲率曲面的区域稳定性。     

Exact and approximate EM estimation of mutually exciting hawkes processes

Motivated by the availability of continuous event sequences that trace the social behavior in a population e.g. email, we believe that mutually exciting Hawkes processes provide a realistic and informative model for these sequences. For complex mutually exciting processes, the numerical optimization used for univariate self exciting processes may not provide stable estimates. Furthermore, convergence can be exceedingly slow, making estimation computationally expensive and multiple random restarts doubly so. We derive an expectation maximization algorithm for maximum likelihood estimation mutually exciting processes that is faster, more robust, and less biased than estimation based on numerical optimization. For an exponentially decaying excitement function, each EM step can be computed in a single $O(N)$ pass through the data, for $N$ observations, without requiring the entire dataset to be in memory. More generally, exact inference is $\Theta (N^{2})$ , but we identify some simple $\Theta (N)$ approximation strategies that seem to provide good estimates while reducing the computational cost.     

A new approach on estimation of the tail indexUne nouvelle méthode pour l'estimation de l'index d'une queue

A new approach on tail index estimation is proposed based on studying the in-sample evolution of appropriately chosen diverging statistics. The resulting estimators are simple to construct, and they can be generalized to address other rate estimation problems as well. To cite this article: D.N. Politis, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 279–282.     

两类修正的Durrmeyer有理插值算子在L_ω~M空间内的逼近（英文）

This paper discusses the approximation problem of two kinds Durrmeyer rational interpolation operators in Orlicz spaces with weight functions,and gives a kind of Jackson type estimation of approximation order by means of continuous modulus, Hardy-Littlewood maximal function, convexity of N function and Jensen inequality.     

Principe de grandes déviations pour l'estimateur de la densité par la méthode des delta-suites

In this Note we obtain pointwise large deviations principle for the delta-sequence method density estimator. A general result is stated for any regular delta-sequence and corollaries with explicit rate functions are derived for delta-sequences, associated to usual estimation methods. The estimation is based upon sequences of independent and identically distributed random variables. To cite this article: N. Berrahou, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

The estimation of moments of an unknown error distribution in the discrete pulse transform

Intuition suggests that the variance of additive noise contaminating a signal can be estimated by investigation of the highest resolution level in a local Nonlinear Multiresolution Analysis. In the case of the Discrete Pulse Transforms with LULU-operators well known elegant identities between B-splines lead to some surprisingly simple and useful results.     

Parametric inference for discrete observations of diffusion processes with mixed effects

Stochastic differential equations with mixed effects provide means to model intra-individual and inter-individual variability in repeated experiments leading to longitudinal data. We consider N i.i.d. stochastic processes defined by a stochastic differential equation with linear mixed effects which are discretely observed. We study a parametric framework with distributions leading to explicit approximate likelihood functions and investigate the asymptotic behavior of estimators under the asymptotic framework : the number N of individuals (trajectories) and the number n of observations per individual tend to infinity within a fixed time interval. The estimation method is assessed on simulated data for various models.