Estimation of Linear Regression Model with Random Coefficients Ensuring Almost Non-Negativity of Variance Estimators

For a linear regression model with random coefficients, this paper considers the estimation of the mean of coefficient vector which, in turn, involves the estimation of variances of random coefficients. The conventional estimation methods for it sometimes provides negative estimates. In order to circumvent this kind of difficulty, a proposal is forwarded and is examined in the light of existing ones.     

Comparing Stochastically Restricted Linear Estimators in a Regression Model

Conditions for superiority of the minimum dispersion estimator over another with respect to the covariance matrix are derived when the vector parameter of a regression model is subject to competing stochastic restrictions. The restrictions may also consist both of a deterministic part and a stochastic part.     

Comparing Stochastically Restricted Estimators in a Linear Regression Model

The minimum dispersion linear unbiased estimators of the vector of parameters in a linear regression model are compared when the parameters of the model are subject to stochastic linear restrictions with different dispersion matrices of the disturbances involved in them.     

选择回归方程自变量的条件数法及其在RK手术中的应用

选择合适的自变量是确定线性回归模型的首要问题,本文以消除自变量之间的复共线性为目标,介绍了一种选择回归方程自变量的条件数法,并在ＲＫ手术的结果预测问题中采用了这一方法。     

A Note on Comparing Stochastically Restricted Linear Estimators in a Regression Model

In his recent paper Liski (1989) derived conditions for superiority of the minimum dispersion estimator over another with respect to the covariance matrix when the parameter vector of a regression model is subject to competing stochastic restrictions. The aim of this note is to provide another necessary and sufficient condition which admits an easier interpretation of superiority related to the covariance matrix criterion.     

On Robust Linear Regression of Hepatic Extraction of Insulin

In classical linear regression model for analysis of medical data concerning hepatic extraction of insulin and c-peptide the fundamental assumption is that the subjects involved are of a similar nature. In reality, if this assumption is violated then the precision of the results is questionable. This paper suggests a robust alternative to overcome this problem. It is observed that the robustification may be a better option to determine an optimal quantity of insulin which minimizes the risk of damage associated with diabatic treatments.     

Insensitivity of Minimax Linear Estimators

If one has prior information on the unknown parameter vector β of a linear model such that ß may be assumed to lie in a concentration ellipsoid, then the resulting minimax linear estimator (MILE) is of ridge type and has smaller quadratic risk than the GLSE. This holds whenever the prior information is a true one. The relation between MILE and GLSE is investigated under incorrect specified prior regions. The MILE is said to be robust against misspecification of the prior region, if its risk stays smaller than the risk of the GLSE.     

Modification of the Minimum Logit Chi-Squared Estimator in Simple Linear Logistic Regression

A new modification of Berkson's minimum logit chi-squared estimator in simple linear logistic regression is suggested in order to achieve reduction of first order bias of the estimator as well as in the model. Furthermore, unlike estimators currently available, our procedure is quite simple to apply in practice and is valid even in the presence of zero frequencies in the table.     

Application of Random Coefficient Regression Model to Myopia Data: A Case Study

A one-year birth cohort from Northern Finland has been followed up since 1966. As a part of this study, we are in this paper concerned with analysing the progression of myopia (nearsightness) up to the age of 20 years. The random coefficient regression model was chosen for the analysis because of the large individual variation in the development of myopia. Maximum likelihood estimates for the parameters in the model were obtained via the expectation maximization (EM) algorithm. It is shown how the estimated model can be used to predict future observations for an individual using the previously recorded refractive error measurements as well as other relevant data on the patient in question.     

Flexible Modelling of the Covariance Matrix in a Linear Random Effects Model

A flexible approach is proposed for modelling the covariance matrix of a linear mixed model for longitudinal data. The method combines parametric modelling of the random effects part with flexible modelling of the serial correlation component. The approach is exemplified on weight gain data and on the evolution of height of children in their first year of life of the Jimma Infant Survival Study, an Ethiopian cohort study. The analyses show the usefulness of the approach.     

On Admissible Estimators in a Linear Model

Let Y be observable random vector such that EY=Xβ and D(Y)=ρ²V. Linear estimation of a parameter p′β under the squared loss is considered. RAO, 1976 and 1979, obtained a necessary and sufficient condition for admissibility of an estimator t′Y in the case X=I. This result will be extended for arbitrary X. AMS 1970 subject classifications. Primary 62J05; secondary 62C15.     

Generalized Confidence Intervals for Ratios of Regression Coefficients with Applications to Bioassays

The problem of constructing a confidence interval for the ratio of two regression coefficients is addressed in the context of multiple regression. The concept of a Generalized Confidence Interval is used, and the resulting confidence interval is shown to perform well in terms of coverage probability. The proposed methodology always results in an interval, unlike the confidence region generated from Fieller's theorem. The procedure can easily be implemented for parallel‐line assays, slope‐ratio assays, and quantal assays under a probit model. Furthermore, this approach can also be extended to compute confidence intervals based on data from multiple bioassays. The results are illustrated using several examples.     

Heteroscedastic Nonlinear Regression Models with Random Effects and Their Application to Enzyme Kinetic Data

We present a new modification of nonlinear regression models for repeated measures data with heteroscedastic error structures by combining the transform-both-sides and weighting model from Caroll and Ruppert (1988) with the nonlinear random effects model from Lindstrom and Bates (1990). The proposed parameter estimators are a combination of pseudo maximum likelihood estimators for the transform-both-sides and weighting model and maximum likelihood (ML) or restricted maximum likelihood (REML) estimators for linear mixed effects models. The new method is investigated by analyzing simulated enzyme kinetic data published by Jones (1993).     

线性随机系统的小波性质

本文分析了线性随机系统解过程的小波特征，得到若干性质，并分析了小波展开系统的统计特征及相关程度．     

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.     

Analysis of Colony-Forming Ability of Human Fibroblast Strains by Linear Regression

A linear regression approach is presented for the statistical analysis of dose-response curves obtained by measuring the colony-forming ability of human fibroblast strains. The crucial determination of the dose range in which the linear model can be assumed is achieved by a combination of statistical criteria and biological claims. As a basic quantitative parameter we investigate the slope of the regression line and, by taking reciprocals, we retransform it into the biologically established parameter D₀. Several methods for the combination of estimates are presented.     

Confidence Estimation of an Unknown Component of the Vector of Regressor Variables in Multivariate Linear Regression

The model used in this paper is Y = Xβ, where with unknown x₀. Estimators of x₀ are derived by putting β_mx₀ =β_m+1 regarding β_m+1 as a new unknown parameter. Formally we use the model Y = X₁β₊ + e where β′₊ = (β₀, …β_m+1 and Then β_m+1/ β_m is a point estimator of x₀. Assuming normality for e and taking the random variable z=β_mx₀?β_m+1 we get a t-distributed variable and finally a confidence estimator of x₀. The formulas are applied in dose response relations in antibiotic assays refering to a standard. Now we can take into account not only the dependence on the dose/concentration but also on the position on the test agar plate where the test solution is filled in. As a consequence the confidence interval of the unknown dose/concentration x₀ becomes shorter and by it the statements more precise.     

Semiparametric Regression in Size-Biased Sampling

Summary .  Size-biased sampling arises when a positive-valued outcome variable is sampled with selection probability proportional to its size. In this article, we propose a semiparametric linear regression model to analyze size-biased outcomes. In our proposed model, the regression parameters of covariates are of major interest, while the distribution of random errors is unspecified. Under the proposed model, we discover that regression parameters are invariant regardless of size-biased sampling. Following this invariance property, we develop a simple estimation procedure for inferences. Our proposed methods are evaluated in simulation studies and applied to two real data analyses.     

Zur Versuchsplanung für Schätzungen im gemischten Modell der linearen Regression1

The covariance matrix of the least-squares-estimator for the coefficients of the mixed model of linear regression is deduced. This serves as a base to work out procedures experimental design for point and confidence estimations of the regression coefficients and the regression function. So it was shown, that the C-, A-, D- and G-optimal designs in the mixed model are the same as in model I. Further an assertion for sample size determination is proved especially for point estimation of the regression function.