A Combined Product Estimator in Sample Survey

For the estimation of the population mean in stratified random sampling a ‘Combined Product Estimator’ is proposed which is more efficient than the ‘Combined Ratio’ and ‘Separate Ratio’ estimators. Also, the proposed estimator have exact expressions for bias and mean square error. An empirical illustration is given to compare the efficiencies of different estimators.     

A Product-Type Estimator in Double Sampling

The use of ratio and product estimators, using auxiliary information, for estimating the mean of a finite population is well known. The efficiency of ratio estimator or product estimator is high depending on whether the auxiliary character is highly positively or negatively coorelated with the main character of interest. This paper proposes a product-type estimator which is more efficient than the usual ratio and product estimators in practical situations. We consider the case of double sampling from which the single sampling results may easily be derived.     

On the Estimation of Population Mean in Stratified Sampling

When stratified random sampling is used for the estimation of population mean, use of ‘Combined ratio estimator’ is well known. Some improved estimators for population mean are proposed which are better than ‘Combined ratio estimator’ and some other well known existing ones, from the point of view of bias and mean square error. An empirical illustration is given.     

二阶段等距抽样

本文提出了二阶段等距抽样的概念．分第二阶段样本为等距抽样和SRSWOR两种情况讨论了总体平均值的估计问题．在第二阶段抽样为SRSWOR情况下,讨论了辅助信息的利用问题,提出了总体平均值的比型估计和回归型估计．并通过一个实际计算的例子,对文中提出的不同估计量进行了比较．     

An Alternative Approach to Estimation in Two-Phase Sampling Using two Auxiliary Variables

Using two-phase sampling mechanism, two alternative estimators in the presence of the available knowledge on second auxiliary variable z are considered, when the population mean of the main auxiliary variable × is unknown. The suggested estimators are found to be more eficient than the ratio-type and regression-type estimators suggested by KIREGYERA (1980, 1984).     

Estimation of Population Regression Coefficient in Successive Sampling

An attempt has been made to derive the theory of successive sampling for estimation of regression coefficient. The situations considered are estimation of regression coefficient for current occasion, estimation of change of regression coefficients over two occasions and estimation of average of regression coefficients over two occasions. The expressions of optimum estimators along with their variances have been worked out. On comparing their efficiencies empirically, it has been observed that similar to the estimation of mean, successive sampling can also be used with advantage for estimation of regression coefficient.     

Improved Generalized Ratio-Cum-Product Estimation

In this paper, a generalized ratio-cum-product estimator for estimating the ratio (product) of two population means using auxiliary information on two other variables is given of which the estimators by SINGH (1969) and SHAH and SHAH (1978) are particular cases. The estimator is regeneralized when the covariance between two auxiliary variables is known.     

Estimation of Partial Regression Coefficient

A sampling scheme providing unbiased partial regression coefficient has been proposed. The proposed sampling scheme is not only unbiased but also superior to simple random sampling and that due to Singh and Bathla (1990) for estimation of partial regression coefficient.     

Some Remarks on the Estimation of Mean in the Normal Population

This paper generalizes the estimator proposed by Searles (1964) and further studied by SRIVASTAVA (1980) and gives some expressions for the first two moments and an integral representation for the α^th raw moment. The latter is found suitable for computational purposes. Some points in SRIVASTAVA'S (1980) paper are also clarified. Efficiencies of 3 estimators belonging to this class are analyzed with respect to the usual sample mean.     

Estimation of a Conditional Mean in a Linear Regression Model after a Preliminary Test on Regression Coefficient

Consider the two linear regression models of Y_ij on X_ij, namely Y_ij = β_io + β_ij, X_ij + E_ij = 1, 2,…, n_i, i = 1, 2, where E_ij are assumed to be normally distributed with zero mean and common unknown variance σ². The problem of estimating the conditional mean of Y₁ for a given value of X₁ is considered when it is a priori suspected that β₁₀ = β₂₀ and β₁₁ = β₂₁. The preliminary test estimator is proposed. The exact expressions for the bias and the mean square error of the estimator are derived. The relative efficiency of the new estimator to the usual least square estimator based on the first regression alone is computed and is used to determine the appropriate value of the significance level of the preliminary test β₁₀ = β₂₀ and β₁₁ = β₂₁.     

A Note on Balanced Sampling and Robust Genetic Predictors

The concept of balanced sampling is applied to prediction in finite samples using model based inference procedures. Necessary and sufficient conditions are derived for a general linear model with arbitrary covariance structure to yield the expansion estimator as the best linear unbiased predictor for the mean. The analysis is extended to produce a robust estimator for the mean squared error under balanced sampling and the results are discussed in the context of statistical genetics where appropriate sampling produces simple efficient and robust genetic predictors free from unnecessary genetic assumptions.     

Overlapping Clusters of Tuberculosis Contacts: An Improved Sampling Strategy

A two stage without replacement strategy is proposed for estimating the population mean of overlapping clusters of contacts of tuberculosis cases. This sampling strategy is an improvement over the two sampling strategies proposed by SINGH (1988). A numerical illustration is provided by taking two populations of tuberculosis contacts from New York City; the percentage gain in efficiency varies from 3.70 to 24.99. The proposed improved sampling strategy may be useful to other contagious diseases in the different fields of biomedical sciences or similar situations in other fields.     

Estimation of a Conditional Mean in a Linear Regression Model

Consider the two linear regression models of Y_ij on X_ij, namely Y_ij = β_io + β_il X_ij + ε_ij,j = 1,2,…,n_i, i = 1,2, where ε_ij are assumed to be normally distributed with zero mean and common unknown variance σ². The estimated value of a mean of Y₁ for a given value of X₁ is made to depend on a preliminary test of significance of the hypothesis β₁₁ = β₂₁. The bias and the mean square error of the estimator for the conditional mean of Y₁ are given. The relative efficiency of the estimator to the usual estimator is computed and is used to determine a proper choice of the significance level of the preliminary test.     

Shrinkage Pre-Test Estimator of the Intercept Parameter for a Regression Model with Multivariate Student-t Errors

In the presence of an uncertain prior information about the value of the slope parameter, the estimation of the intercept parameter of a simple regression model with a multivariate Student-t error distribution is investigated. The unrestricted, restricted and shrinkage preliminary test maximum likelihood estimators are defined. The expressions for the bias and the mean square error of the three estimators are provided and the relative efficiences are analyzed. A maximin criterion is established, and graphs are constructed for an arbitrary number of degrees of freedom (D.F.) as well as sample sizes. A criterion to select optimal significance level is also discussed.     

A Note on the Estimation of the Population Mean in Stratified Random Sampling Using Two Auxiliary Variables

In this paper, a two‐phase sampling estimator for a stratified population mean using two auxiliary variables x and z is considered when the stratum mean of x is unknown but that of z is known. The suggested estimator under its optimal condition is found to be more efficient than the one using only x.     

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.     

A Study of Second Order Approximation of Some Ratio Type Strategies

For estimating the mean of a finite population using information on an auxiliary variable, the conventional ratio strategies and strategies due to Srivastava (1967), Reddy (1973), Gupta (1978), Sahai (1979) and Adhvaryu-Gupta (1983) have been studied. Asymptotic expressions for the second order approximations of biases and mean square errors of these strategies have been obtained. The suitability of these strategies have been discussed with the help of live data.     

Almost Unbiased Ratio and Product Type Estimators: A New Approach

In this paper, we have proposed a new method, consisting of a linear variety of the estimators and a linear constraint to remove the bias appearing in the estimators of the ratio R = Y/X and product P = YX. The percent relative efficiency of proposed estimators has also been demonstrated with numerical illustrations.