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.     

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.     

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.     

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.     

Testable Hypotheses Implied by a Linear Hypothesis

ROY and ROY have shown that for any linear hypothesis H being not testable it is possible to construct a testable hypothesis which is implied by H. A maximal testable hypothesis implied by H is presented.     

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.     

Least Squares and Minimum MSE Estimators of Variance Components in Mixed Linear Models

The paper deals with the quadratic invariant estimators of the linear functions of variance components in mixed linear model. The estimator with locally minimal mean square error with respect to a parameter ? is derived. Under the condition of normality of the vector Y the theoretical values of MSE of several types of estimators are compared in two different mixed models; under a different types of distributions a simulation study is carried out for the behaviour of derived estimators.     

Classification of Trends Via the Linear State Space Model

A method is presented for classification of trend curves based on the linear state space model. In this approach information about the smoothness of the trend curves is incorporated into the classification model by a nonstationary stochastic trend model and can thereby be used to obtain a better classification. In the case of small data sets the performance of the classification is significantly improved in comparison with the usual cluster analysis. Maximum likelihood estimation can be used to calculate the parameters of this model and to determine the classification. The classification algorithm is described in detail and the results are compared to those of the usual cluster analysis by simulation studies and by an application to tree ring data.     

Small area estimation when auxiliary information is measured with error

Small area estimation methods typically combine direct estimatesfrom a survey with predictions from a model in order to obtainestimates of population quantities with reduced mean squarederror. When the auxiliary information used in the model is measuredwith error, using a small area estimator such as the Fay–Herriotestimator while ignoring measurement error may be worse thansimply using the direct estimator. We propose a new small areaestimator that accounts for sampling variability in the auxiliaryinformation, and derive its properties, in particular showingthat it is approximately unbiased. The estimator is appliedto predict quantities measured in the U.S. National Health andNutrition Examination Survey, with auxiliary information fromthe U.S. National Health Interview Survey.     

Information in Observation Under the Correlated Linear Model

In this paper we propose a measure of information in a set of observations under a given design and the linear model with the observations being correlated. We then compare the different sets of observations with respect to the information measure in the situations where the underlying designs are nested and split-plot. AMS 1970 Subject Classification: Secondary 62J05, 62J10, 62K05, 62K10, 62K15, 62K99.     

雪菜的亚硝酸盐含量-线性模型与神经网络

亚硝酸盐含量直接影响雪菜食用的安全性．利用正交试验对雪菜腌制过程中影响亚硝酸盐含量变化的若干因素进行研究,建立数学模型,包括线性模型与神经网络模型．     

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。     

Unbiasedness of Iterated Aitken Estimators

The iterated Aitken estimator of the parameter vector of the general linear model is shown to be unbiased on the assumption that the errors underlying the model follow a symmetric probability law with mean zero.