Adaptive Estimation of the Integral of Squared Regression Derivatives

A problem of estimating the integral of a squared regression function and of its squared derivatives has been addressed in a number of papers. For the case of a heteroscedastic model where smoothness of the underlying regression function, the design density, and the variance of errors are known, the asymptotically sharp minimax lower bound and a sharp estimator were found in Pastuchova & Khasminski (1989). However, there are apparently no results on the either rate optimal or sharp optimal adaptive, or data-driven, estimation when neither the degree of regression function smoothness nor design density, scale function and distribution of errors are known. After a brief review of main developments in non-parametric estimation of non-linear functionals, we suggest a simple adaptive estimator for the integral of a squared regression function and its derivatives and prove that it is sharp-optimal whenever the estimated derivative is sufficiently smooth.     

FPK法在集总参数系统随机温度研究中的应用

应用FPK法研究了集总参数系统在对流和辐射环境下温度随机变化的规律。设激励是均值为0的白噪声且系统参数为常量，在与环境对流换热时，系统随机温度的均值不变，方差与系统时间常数的平方根成反比；在与环境辐射换热时，系统随机温度一般不呈正态分布，其中均值，均方值还与系统确定性温度有关，由此可知，当存在随机激励时，用有热惯性的测温系统精确测定动态温度是不可能的。     

随机-无标度统一混合演化网络模型

根据实际网络的特点,提出了一个随机-无标度统一混合演化网络模型.通过引入一个调节参数p将随机演化网络与(Barabási-Albert)无标度网络统一起来.理论计算和计算机模拟表明,当调节参数p从1变化到0时,网络结构实现了从随机演化网络到BA无标度网络的连续过渡.     

关于岩石破碎的三角形效应研究

本文从分形几何学的角度研究了岩石的断裂规律，从理论上论述了岩石破碎的三角形效应，并给出了一般岩石破碎的数学模型．     

一种定量敏感性问题的随机化调查方法

在敏感性问题的随机化调查中,既有调查个体是否具有敏感属性的二值敏感性问题,即属性特征问题,又有调查特定人群中敏感指标量的“多少”问题,即定量特征敏感性问题.对于定量特征敏感性问题的调查,E ichhorn,H aryre于1983年提出了一种随机化调查方法,并给出了定量敏感问题指标量均值的一个无偏估计.本文提出一种定量特征敏感性问题的随机化调查方法,得到的结果表明,本文提出的方法优于E ichhorn,H aryre(1983)提出的方法.     

关于不定方程x^3-1=Dy^2

证明了如下结果：如果题设方程有非平凡整数解，D只有唯一的6k＋1形素因子p，则D要么没有其他素因子，要么任何其他素因子q都满足（3p／q）=1或（p／q）=1。     

Bootstrapping data with multiple levels of variation

The authors consider general estimators for the mean and variance parameters in the random effect model and in the transformation model for data with multiple levels of variation. They show that these estimators have different distributions under the two models unless all the variables have Gaussian distributions. They investigate the asymptotic properties of bootstrap procedures designed for the two models. They also report simulation results and illustrate the bootstraps using data on red spruce trees.     

电磁-温度耦合条件下推力磁轴承涡流损耗分析

针对一类以实心推力盘为主要热源的电磁轴承转子系统，研究了电磁-温度耦合条件下从线圈加电到稳定运行整个过程中的电磁场，给出了电磁场涡流损耗的解析计算方法．通过将实例的计算结果与有限元方法及实验结果对比表明，采用该解析计算方法可简单、快捷及准确地解决系统初步设计时的参数选定问题．     

A Mixed Model Approach for Geoadditive Hazard Regression

Abstract.  Mixed model based approaches for semiparametric regression have gained much interest in recent years, both in theory and application. They provide a unified and modular framework for penalized likelihood and closely related empirical Bayes inference. In this article, we develop mixed model methodology for a broad class of Cox-type hazard regression models where the usual linear predictor is generalized to a geoadditive predictor incorporating non-parametric terms for the (log-)baseline hazard rate, time-varying coefficients and non-linear effects of continuous covariates, a spatial component, and additional cluster-specific frailties. Non-linear and time-varying effects are modelled through penalized splines, while spatial components are treated as correlated random effects following either a Markov random field or a stationary Gaussian random field prior. Generalizing existing mixed model methodology, inference is derived using penalized likelihood for regression coefficients and (approximate) marginal likelihood for smoothing parameters. In a simulation we study the performance of the proposed method, in particular comparing it with its fully Bayesian counterpart using Markov chain Monte Carlo methodology, and complement the results by some asymptotic considerations. As an application, we analyse leukaemia survival data from northwest England.     

α-Al_2O_3中三角Ru~(3+)中心的g因子研究

基于晶体场模型,采用三角对称下4d5离子各向异性g因子微扰公式,对α-Al2O3中三角Ru3+中心的电子顺磁共振实验结果进行了理论研究。计算中利用较新的Ru3+自由离子旋轨耦合参数,考虑了轨道缩小因子和旋轨耦合参数对杂质Ru3+中心g因子的影响,讨论了Ru3+中心的局部结构性质,结果表明理论与实验符合得很好。