Poduri S. R. S. Rao

Estimators for the One-Way Random Effects Model with Unequal Error Variances

Abstract Using the random effects model, yij = μ + α i + ∈ ij , (i = 1, …, k; j = 1, …, ni ), where α i and ∈ ij are normal with means zero and variances σα 2 and σ i 2, this article considers eight methods of estimating σ i 2, σα 2, and thirteen corresponding procedures of estimating μ. Biases and mean squared errors (MSEs) of these procedures are examined for variations in the magnitudes of the unknown parameters, the sample sizes, and the number of groups.

Generalized Multivariate Estimator for the Mean of Finite Populations

Abstract Just as ratio estimators are often indicated when the variable y is positively correlated with an auxiliary variable x so product estimators are indicated when y is negatively correlated with x. The method of estimation suggested by Olkin [4] is extended to the case where some or all of the auxiliary variables are positively correlated and some or all are negatively correlated with y.

Three modifications of the principle of the minque

Nonnegative estimators for the variance components of a linear model are obtained by ignoring the condition for unbiasedness in the principle of the MINQUE. An estimator is derived when the priori weights are proportional to the variance components. The ordinary sample variance is shown to be the nonnegative MINQUE. Efficiencies of the three estimators are examined for some special cases of the model.

W.G. Cochran's impact on statistics

Sampling and Observational Studies. Public Health and Biometrics. Categorical Data. Analysis of Variance and Design of Experiments. Variance Components. Some Philosophical Issues. Theoretical Developments. Index.

Comparison of Four Ratio-Type Estimates under a Model

Abstract Mean square errors of the simple ratio estimate, the estimate obtained by Quenouilles method of bias reduction, Goodman and Hartleys estimate and the estimate proposed by Hartley are compared.

The three-fold nested random effects model

Abstract Estimation of the variance components and the mean of the balanced and unbalanced threefold nested design is considered. The relative merits of the following procedures are evaluated: Analysis of variance (ANOVA), maximum likelihood (ML), restricted maximum likelihood (REML), and minimum variance quadratic unbiased estimator (MIVQUE). A new procedure called the weighted analysis of means (WAM) estimator which utilizes prior information on the variance components is proposed. It is found to have optimum properties similar to the REML and MIVQUE, and it is also computationally simpler. For the mean, the overall sample average, grand mean, unweighted mean, and generalized least-squares (GLS) estimator with its weights obtained from the above estimators for the variance components are considered. Comparisons of the above procedures for the variance components and the mean are made from exact expressions for the biases and mean square errors (MSEs) of the estimators and from empirical investigations.

Efficiencies of Nine Two-Phase Ratio Estimators for the Mean

Abstract Nine two-phase ratio estimators for the mean of a finite population are presented. Assuming a linear model, exact expressions for their biases and mean squared errors are derived. Then the nine estimators are compared as to bias and mean squared error. The list of estimators includes the Jackknife estimator and four modifications; two of the proposed modifications are implemented by first expressing the classical estimator in the form of a regression estimator.

On the Two-Phase Ratio Estimator in Finite Populations

Abstract Modified ratio estimators for the mean are proposed for the case in which the first- and second-phase samples are drawn without replacement and independent of each other. Conditions for these estimators to be more efficient than the classical estimator are investigated. Two methods for evaluating the expectation of the reciprocal of the number of distinct units are presented.

Anova and minque type of estimators for the one-way random effects model

The one-way random effects model with unequal variances and unequal sample sizes is considered. Estimation of the variances, variance of a single observation (total variance), and the standard error of the unweighted mean are considered. Precision of the Analysis of Variance and Unweighted Sums of Squares type of estimators and the Minimum Norm Quadratic Unbiased Estimators with a priori weights are examined.

ESTIMATION OF THE MEAN SQUARE ERROR OF THE RATIO ESTIMATOR

The conventional and weighted least squares estimators and a simplified version of the jackknife estimator for the mean square error of the ratio estimator of a finite population mean are considered. The biases and the mean square errors of these estimators are compared under a suitable linear regression model.