测试－计算数据综合处理方法之研究

求解由控制方程和初始、边界条件组成的导热问题，从数学意义上讲其解是单值的．然而当广合信息的方程个数多于未知量个数时就会导致较多的解的可能性．本文采用测试－计算数据综合处理法来确定其近真值，改善了测试值的不确定度．     

最小二乘估计的一种算法

众所周知,最小二乘估计(LSE)是广泛应用的一种重要数学工具。本文介绍一种新算法,当待估参数的数目超过方程总数的一半时,它比常规算法节省运算量。本算法的另一个特点是残差计算待估参数的 LSE,并由此揭示了残差的一些重要性质。     

一种基于运动估计的隔行/逐行转换算法

针对从隔行扫描的电视场图像获得高质量的逐行扫描帧图像,提出了一种从隔行扫描到逐行扫描的转换算法。该算法通过在隔行/逐行转换中引入运动估计技术,找出相邻两场图像间的运动矢量,然后在场间行内插值时进行图像调整来消除由于图像错位引起的运动模糊,生成具有高垂直分辨率的逐行图像。算法中针对这一特定应用场合,设计了一种运动估计方法。     

Bayes minimax estimation of a bernoulli p in a restricted parameter space

In many estimation problems the parameter of interest is known,a priori, to belong to a proper subspace of the natural parameter space. Although useful in practice this type of additional information can lead to surprising theoretical difficulties. In this paper the problem of minimax estimation of a Bernoulli pwhen pis restricted to a symmetric subinterval of the natural parameter space is considered. For the sample sizes n = 1,2,3, and 4 least favorable priors with finite support are provided and the corresponding Bayes estimators are shown to be minimax. For n = 5 and 6 the usual constant risk minimax estimator is shown to be the Bayes minimax estimator corresponding to a least favorable prior with finite support, provided the restriction on the parameter space is not too tight.     

The Empirical Likelihood for First-Order Random Coefficient Integer-Valued Autoregressive Processes

This article studies the empirical likelihood method for the first-order random coefficient integer-valued autoregressive process. The limiting distribution of the log empirical likelihood ratio statistic is established. Confidence region for the parameter of interest and its coverage probabilities are given, and hypothesis testing is considered. The maximum empirical likelihood estimator for the parameter is derived and its asymptotic properties are established. The performances of the estimator are compared with the conditional least squares estimator via simulation.     

Efficiency of least squares estimators in the presence of spatial autocorrelation

The effect of spatial autocorrelation on inferences made using ordinary least squares estimation is considered. It is found, in some cases, that ordinary least squares estimators provide a reasonable alternative to the estimated generalized least squares estimators recommended in the spatial statistics literature. One of the most serious problems in using ordinary least squares is that the usual variance estimators are severely biased when the errors are correlated. An alternative variance estimator that adjusts for any observed correlation is proposed. The need to take autocorrelation into account in variance estimation negates much of the advantage that ordinary least squares estimation has in terms of computational simplicity     

Bootstrapping time series models

This paper surveys recent development in bootstrap methods and the modifications needed for their applicability in time series models. The paper discusses some guidelines for empirical researchers in econometric analysis of time series. Different sampling schemes for bootstrap data generation and different forms of bootstrap test statistics are discussed. The paper also discusses the applicability of direct bootstrapping of data in dynamic models and cointegrating regression models. It is argued that bootstrapping residuals is the preferable approach. The bootstrap procedures covered include the recursive bootstrap, the moving block bootstrap and the stationary bootstrap.     

Bayesian ikference procedures derived via the concept of relative surprise

We consider the problem of deriving Bayesian inference procedures via the concept of relative surprise. The mathematical concept of surprise has been developed by I.J. Good in a long sequence of papers. We make a modification to this development that permits the avoidance of a serious defect; namely, the change of variable problem. We apply relative surprise to the development of estimation, hypothesis testing and model checking procedures. Important advantages of the relative surprise approach to inference include the lack of dependence on a particular loss function and complete freedom to the statistician in the choice of prior for hypothesis testing problems. Links are established with common Bayesian inference procedures such as highest posterior density regions, modal estimates and Bayes factors. From a practical perspective new inference procedures arise that possess good properties.     

A note on the unified theory of least squares

The general form of a matrix which appears in the normal equation for estimating parameters in the Gauss-Markoff linear model has been obtained.     

Bayesian least squares estimates of univariate regression functions

The regression function R(?) to be estimated is assumed to have an expansion in terms of specified functions, orthogonalized vich respect to values of the explanatory variable. Relative precisions of OBSERVATION are assumed known. The estimate is the posterior linear mean of R(?) given the data. The investigator plots graphs of appropriate functions as an aid in eliciting his prior means and precisions for the coefficients in the expansion. The method is illustrated by an example using simulated data, an example in which effects of various dosages of Vitamin D are estimated, and an example in which a utility function is estimated.