Improved Estimation of Coefficients in Regression Models with Incomplete Prior Information

The method of mixed regression is considered for the estimation of coefficients in a linear regression model when incomplete prior information is available, and two families of improved estimators stemming from Stein-rule are proposed. Their properties are studied when disturbances are normal but small.     

Optimal Experimental Design and Accuracy of Parameter Estimation for Nonlinear Regression Models Used in Long-term Selection

An experimental design problem is considered for the analysis of long-term selection experiments with nonlinear regression models. For a 3-parametric exponential regression function whose parameters have also a reasonable biological interpretation approximate formulas for the determination of the necessary number of observations at each generation are constructed in such a way that the half expected length of an (1 — α)-confidence interval for a chosen parameter is not greater than a given value. In this sense the accuracy of the parameter estimators can be described.     

A Method of Estimation of Change Points in Multiphasic Growth Models

The least-squares estimation (LSE) of change points and the phase parameters is considered for two growth models with piecewise continuously connected exponential and stationary phases. The calculation of a LSE is reduced to the solution of a finite number of simpler least-squares problems for which methods of calculation are well known.     

Parameter Estimation for the Bateman Function via Moments of the Empirical Curve

The parameters of the function f(t)=c(e^?at-e^?bt) are related in a simple way to the moments ^∞ tⁿf(t)^dt(n=0, 1, 2). Using empirical values of f, the moments can be estimated by numerical integration. Therefrom estimates of the parameters are obtained by elementary algebra.     

A Bayesian Decision Procedure for Selecting Prognostic Variables Associated with Survival for Data in which Censoring is Prevalent

A Bayesian procedure is developed for the selection of concomitant variables in survival models. The variables are selected in a step-up procedure according to the criterion of maximum expected likelihood, where the expectation is over the prior parameter space. Prior knowledge of the influence of these covariates on patient prognosis is incorporated into the analysis. The step-up procedure is stopped when the Bayes factor in favor of omitting the variable selected in a particular step exceeds a specified value. The resulting model with the selected variables is fitted using Bayes estimates of the coefficients. This technique is applied to Hodgkin's disease data from a large Cooperative Clinical Trial Group and the results are compared to the results from the classical likelihood selection procedure.     

Fidelity Estimation for a Hierarchical Classifier

To estimate the correct classification rate of a classifier, many different methods exist (test sample, bootstrap, cross validation). The test sample is a method with very small expense. Sometimes, only a small number of objects is available (seldom diseases, high costs for experiments). When we split the sample in training set and test set, we get good or bad fidelity estimations but, unfortunately, vice versa a big or small confidence interval for the estimation. Overcoming this dilemma is only possible for simple classifiers. Such a simple classifier is investigated and a direct fidelity estimation is proposed.     

On the Estimation of the Nearest Neighbour Distribution,G(t), for Point Processes

A new method is proposed for estimating G(t), the distribution function of the distance from an object to its nearest neighbour in a spatial point process. The new method makes more complete use of the information available and has a smaller mean squared error than that of the existing alternatives. The method appears equally effective with random, clustered and regular patterns.     

科尔沁沙地植被恢复中差不嘎蒿种群不同龄级个体的点格局分析

差不嘎蒿（Artemisia halodendron）主要分布在呼伦贝尔沙地和科尔沁沙地的流动和半固定沙丘上,是良好的乡土固沙半灌木,也是退化沙地固定和植被恢复过程中的建群种。点格局分析方法是20世纪末发展起来的多尺度空间格局分析方法。通过对差不嘎蒿种群的点格局分析,发现差不嘎蒿幼体的空间格局多为集群分布,在各个尺度上都极为显著,而随着差不嘎蒿龄级的增加,其空间分布也逐渐显现为随机分布。差不嘎蒿相邻龄级的空间关系差异不显著,而间隔龄级间则呈空间负相关。这与其幼体聚集,成体随机分布的空间格局相一致。     

Calculating the Sample Size in the Examination of Animals for the Presence of Residues Using Prior Information

The council of the European Economic Communities has issued a directive (86/469/EEC) for the examination of animals and fresh meat for the presence of residues of several hormones, drugs and environmental pollutants. The purpose of this paper is to compare the method used by the EEC with a Bayesian approach to calculate necessary sample size using prior information in different situations (assuming Beta-, Normal- and Gamma-distribution for the prior distribution). It has been shown that the Bayesian approach requires significantly smaller sample sizes for all levels of inspection. Furthermore, an example is given in the examination of pigs for the presence of residues of drugs in pork.     

删失数据下非线性半参数回归模型中参数的经验似然推断

考察了响应变量在随机删失情形下的非线性半参数回归模型,构造了未知参数的经验对数似然比统计量和调整经验对数似然比统计量,证明在一定条件下,所构造的经验似然比统计量渐近于X~2分布,并由此构造出未知参数的置信域.此外,又构造了未知参数的最小二乘估计量,证明了它的渐近性质.通过模拟研究表明,经验似然方法在置信域的覆盖概率以及精度方面要优于最小二乘法.     

Function Switching as a Basis for Bursts of Rapid Change During the Evolution of Pituitary Growth Hormone

Pituitary growth hormone shows a pattern of molecular evolution in which occasional bursts of rapid change are imposed on a slow basal rate. It is suggested that these bursts of rapid evolution are a consequence of acquisition by this protein hormone of a secondary function, the importance of which varies. As the function of the hormone switches to accommodate the changes in role, its structure will also alter, adapting it to acquisition or loss of the secondary function. Several rounds of such ``function switching' could give a substantial change in structure (the sum of several small changes) with little overall change in function. A similar process could underlie rapid bursts of evolution in other proteins. Received: 15 July 1996 / Accepted: 19 September 1996     

Estimation of total body volume from arm measurements in Punjabi girls aged 10–19 years

Mean values and standard deviations of total body volume, body density, arm volume, height, weight and a battery of 15 measurements of arm comprising different lengths, girths, diameters and skinfolds of 200 Punjabi girls aged 10–19 years are presented. Relationship between arm volume and total body volume in different age groups are also studied. Highly significant and positive correlations existed between arm volume and total body volume and the values of correlation coefficients r ranged between 0.78 to 0.92 in different age groups. Body volume was estimated also from arm measurements by using selective stepwise multiple linear regression analysis for each age group. Highly significant multiple correlation coefficients R were obtained for predicting total body volume from arm measurements and the values of multiple R ranged between 0.92 to 0.97 in different age groups even with a combination of just three or four arm measurements. The most commonly selected measurements up to fourth step in most of the age groups were upper arm girth and maximum forearm girth.     

Inference for the Break Point in Segmented Regression with Application to Longitudinal Data

This paper considers inference for the break point in the segmented regression or piece‐wise regression model. Standard likelihood theory does not apply because the break point is absent under the null hypothesis. We use results by Davies for this type of non‐standard set‐up [Biometrika 64 (1977), 247–254 and 74 (1987), 33–43] to obtain a test for the null hypothesis of no break point. A confidence interval can be constructed provided replicate data are available. The methods are exemplified using two longitudinal datasets, the one from ecology, the other from pharmacology.