Tests and Confidence Intervals for an Extended Variance Component Using the Modified Likelihood Ratio Statistic

Abstract.  The large deviation modified likelihood ratio statistic is studied for testing a variance component equal to a specified value. Formulas are presented in the general balanced case, whereas in the unbalanced case only the one-way random effects model is studied. Simulation studies are presented, showing that the normal approximation to the large deviation modified likelihood ratio statistic gives confidence intervals for variance components with coverage probabilities very close to the nominal confidence coefficient.     

Approximate optimal allocation in repeated sampling from a finite population

Samples of size n are drawn from a finite population on each of two occasions. On the first occasion a variate x is measured, and on the second a variate y. In estimating the population mean of y, the variance of the best linear unbiased combination of means for matched and unmatched samples is itself minimized, with respect to the sampling design on the second occasion, by a certain degree of matching. This optimal allocation depends on the population correlation coefficient, which previous authors have assumed known. We estimate the correlation from an initial matched sample, then an approximately optimal allocation is completed and an estimator formed which, under a bivariate normal superpopulation model, has model expected mean square error equal, apart from an error of order n^-2, to the minimum enjoyed by any linear, unbiased estimator.     

Random Bernstein Polynomials

Random Bernstein polynomials which are also probability distribution functions on the closed unit interval are studied. The probability law of a Bernstein polynomial so defined provides a novel prior on the space of distribution functions on [0, 1] which has full support and can easily select absolutely continuous distribution functions with a continuous and smooth derivative. In particular, the Bernstein polynomial which approximates a Dirichlet process is studied. This may be of interest in Bayesian non-parametric inference. In the second part of the paper, we study the posterior from a "Bernstein–Dirichlet" prior and suggest a hybrid Monte Carlo approximation of it. The proposed algorithm has some aspects of novelty since the problem under examination has a "changing dimension" parameter space.     

凝聚随机算子的一个不动点定理

利用拓扑度的基本性质，给出了凝聚随机算子的一个不动点定理，由此推广了Altman定理，为进一步研究随机算子方程解的存在唯一性及解的近似方法提供了一个有力的工具。     

AN ALGORITHMIC APPROACH TO BAYESIAN LINEAR MODEL CALCULATIONS

A framework is described for organizing and understanding the computations necessary to obtain the posterior mean of a vector of linear effects in a normal linear model, conditional on the parameters that determine covariance structure. The approach has two major uses; firstly, as a pedagogical tool in the derivation of formulae, and secondly, as a practical tool for developing computational strategies without needing complicated matrix formulae that are often unwieldy in complex hierarchical models. The proposed technique is based upon symbolic application of the sweep operator SWP to an appropriate tableau of means and covariances. The method is illustrated with standard linear model specifications, including the so-called mixed model, with both fixed and random effects.     

A Spatial-temporal Model for Temperature with Seasonal Variance

We propose a spatial-temporal stochastic model for daily average surface temperature data. First, we build a model for a single spatial location, independently on the spatial information. The model includes trend, seasonality, and mean reversion, together with a seasonally dependent variance of the residuals. The spatial dependency is modelled by a Gaussian random field. Empirical fitting to data collected in 16 measurement stations in Lithuania over more than 40 years shows that our model captures the seasonality in the autocorrelation of the squared residuals, a property of temperature data already observed by other authors. We demonstrate through examples that our spatial-temporal model is applicable for prediction and classification.     

检测系统分辨力定量计算的研究

分辨力是传感器和测量仪器的重要技术参数。数字仪器的分辨力通常取决于内部模数转换器的位数,但如何确定由仪器和传感器组成的检测系统的分辨力,目前尚未见到与之相关的专门性研究成果。该文论证了检测系统的分辨力只与随机误差相关,要提高分辨力就必须减小测量结果的随机波动。通过实验提出了检测系统分辨力的定量计算公式,并证明了其置信概率大于90.9%。     

干线战术通信网的抗毁模型研究

介绍了抗毁通信网分析与设计的原理和方法、针对干线战术通信网中节点移动会导致网络拓扑结构发生变化的特点,提出了动态网络拓扑设计模型和衡量干线战术通信网的抗毁性能的数学模型—随机图模型和齐次随机图模型、计算机模拟结果验证了随机图模型和齐次随机图模型的正确性.     

A semiparametric method of multiple imputation

In this paper, we describe how to use multiple imputation semiparametrically to obtain estimates of parameters and their standard errors when some individuals have missing data. The methods given require the investigator to know or be able to estimate the process generating the missing data but requires no full distributional form for the data. The method is especially useful for non-standard problems, such as estimating the median when data are missing.