An Efficient Regression Type Estimator in Survey Sampling

For the estimation of population mean in simple random sampling, an efficient regression-type estimator is proposed which is more efficient than the conventional regression estimator and hence than mean per unit estimator, ratio and product estimators and many other estimators proposed by various authors. Some numerical examples are included for illustration.     

On the mean square error associated with adaptive generalized ridge regression

Some numerical results are presented for generalized ridge regression where the additive constants are based on the data. The adaptive estimator so obtained is compared with the least-squares estimator on the basis of mean square error (MSE). It is shown that the MSE of each component of the vector of ridge estimators may be as low as 47.1% of the variance of the corresponding component of the least squares vector or as high as 125.2%.     

A General Class of Ratio‐Type Estimators Under Super‐Population Model

The problem of constructing classes of estimators for population mean has been widely discussed by various authors under design approach in sample surveys. An attempt by Upadhyaya , Singh , and Vos (1985) has been made to combine the usual mean and ratio estimator with suitable weights in order to define a general class of estimators. This paper is an attempt to study properties of the same estimator under super‐population model. Optimum weights have also been proposed. Results have been supported with some numerical examples.     

Improvement of Ratio-Type Estimators-II

This paper generalizes the results of AGARWAL (1980) and AGARWAL and KUMAR (1985) by constructing a multivariate ratiotype estimator which, to a first order of approximation, is as efficient as the regression estimator.     

Shrinkage and Pretest Nonparametric Estimation of Regression Parameters from Censored Data with Multiple Observations at Each Level of Covariate

A simple linear regression model is considered where the independent variable assumes only a finite number of values and the response variable is randomly right censored. However, the censoring distribution may depend on the covariate values. A class of noniterative estimators for the slope parameter, namely, the noniterative unrestricted estimator, noniterative restricted estimator and noniterative improved pretest estimator are proposed. The asymptotic bias and mean squared errors of the proposed estimators are derived and compared. The relative dominance picture of the estimators is investigated. A simulation study is also performed to asses the properties of the various estimators for small samples.     

两阶抽样中比率型估计量的平均精度

本文给出了两阶抽样中总体均值的比率型估计量的平均精度,它当样本容量充分大时主项不劣于无偏估计量的平均精度．     

On a Class of Almost Unbiased Ratio Estimators

A class of almost unbiased ratio estimators for population mean σ is derived by weighting sample σ = (1/n) σ y_i, ratio estimators σ and an estimator, σ (y_i/x_i). It is shown that NIETO DE PASCUAL (1961) estimator is a particular member of the class and an optimum estimator in the class (in the minimum variance sense) is identified. The results are illustrated through two numerical examples.     

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.     

On Combination of Ratio and PPS Estimators

AGARWAL and KUMAR (1980) proposed an estimator, combining ratio and pps estimators of population mean and proved that the proposed estimator would always be better (in minimum mean square error sense) than the pps estimator or the ratio estimator under pps sampling scheme for optimum value of constant k (parameter). The optimum value of k is rarely known in practice, hence the alternative is to replace k from the sample-values. In this paper, an estimator depending on estimated optimum value of k based on sample-values, under pps sampling scheme is proposed and studied.     

A New Exponential Ratio-Type Estimator with Linear Combination of Two Auxiliary Variables

In sample surveys, it is usual to make use of auxiliary information to increase the precision of estimators. We propose a new exponential ratio-type estimator of a finite population mean using linear combination of two auxiliary variables and obtain mean square error (MSE) equation for proposed estimator. We find theoretical conditions that make proposed estimator more efficient than traditional multivariate ratio estimator using information of two auxiliary variables, the estimator of Bahl and Tuteja and the estimator proposed by Abu-Dayeh et al. In addition, we support these theoretical results with the aid of two numerical examples.     

二次等距抽样

本文提出了一种二次等距抽样方法,并提出了总体平均值的一个估计量：拼配部分的比型估计与轮换部分的样本均值的加权平均。当样本量较大时,求出了估计量的方差及最优轮换比．并对特殊情形进行了讨论和数值比较．     

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.     

Dimension reduction in survival regressions with censored data via an imputed spline approach

Dimension reduction methods have been proposed for regression analysis with predictors of high dimension, but have not received much attention on the problems with censored data. In this article, we present an iterative imputed spline approach based on principal Hessian directions (PHD) for censored survival data in order to reduce the dimension of predictors without requiring a prespecified parametric model. Our proposal is to replace the right-censored survival time with its conditional expectation for adjusting the censoring effect by using the Kaplan-Meier estimator and an adaptive polynomial spline regression in the residual imputation. A sparse estimation strategy is incorporated in our approach to enhance the interpretation of variable selection. This approach can be implemented in not only PHD, but also other methods developed for estimating the central mean subspace. Simulation studies with right-censored data are conducted for the imputed spline approach to PHD (IS-PHD) in comparison with two methods of sliced inverse regression, minimum average variance estimation, and naive PHD in ignorance of censoring. The results demonstrate that the proposed IS-PHD method is particularly useful for survival time responses approximating symmetric or bending structures. Illustrative applications to two real data sets are also presented.     

A Class of Almost Unbiased Estimators for Finite Populations Mean Using Two Auxiliary Variables

For estimating finite population mean -Y₀ of study character y₀, a class of almost unbiased estimators applying jackknife technique envisaged by Quenouille (1956) is derived. Optimum unbiased estimator (OUE) is also investigated with its variance formula. An empirical study is carried out to demonstrate the performance of the constructed estimator over the usual unbiased estimator, Srivastava (1965), Singh (1967), Singh and Biradar (1992), Tracy , Singh , and Singh (1996) and other almost unbiased estimators.     

Estimation of Residual Valve Gradient from Incomplete Data with Outliers

An important indicator for the long-term recovery after valve replacement surgery is postoperative valve gradient. This information is available only for patients received catheterization or echocardiogram postoperatively. It is plausible that sicker patients are more inclined to undergo these postoperative procedures and their valve gradients tend to be higher. Under this situation, ignoring the missing values and using sample mean based on the available information as an estimate of the whole study population leads to overestimation. Regression estimator is a reasonable choice to eliminate this bias if independent (explanatory) variables closely associated with both residual valve gradient and non-response mechanism can be identified. Using a series of patients receiving St. Jude Medical prosthetic valves, we found that valve area index can be used as an independent variable in the regression estimator. Two digressions from the standard assumptions used in linear regression, heteroscedastic trend of the error term and outliers were found in the data set. Iteratively reweighted least square (IRLS) was adopted to handle heteroscedasticity. Influence function approach was used to evaluate the sensitivity of outliers in regression estimator. Under an equal response rate mechanism, IRLS not only solves the problem of heteroscedasticity, but is also less sensitive to outliers.     

Improved Estimation of Heritability Through Scaling

Two minimum mean square error estimators of heritability are proposed and compared with the conventional regression estimator with live data.     

Relative Efficiency of Estimators of the Mean of a Normal Distribution when Coefficient of Variation is Known

A biased but simple and consistent estimator of the parameter ? has been obtained for the normal distribution N(?, a?₂), ?>0 where a is a known constant. It is shown that the estimator is more efficient than the sample mean or any suitably chosen constant multiple of the sample standard deviation. It is also proved to be more efficient than the mimumum variance unbiased estimator among a typical class of unbiased estimators derived by RASUL KHAN (1968).     

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.     

Improved Shrinkage Estimation of Relative Potency

This article considers the asymptotic estimation theory for the log relative potency in a symmetric parallel bioassay when uncertain prior information about the true log relative potency is assumed to be a known quantity. Three classes of point estimation, namely, the unrestricted estimator, the shrinkage restricted estimator and shrinkage preliminary test estimator are proposed. Their asymptotic mean squared errors are derived and compared. The relative dominance picture of the estimators is presented. Interestingly, proposed shrinkage preliminary test estimator dominates the unrestricted estimator in a range that is wider than that of the usual preliminary test estimator. Most importantly, the size of the preliminary test is much appropriate than the usual preliminary test estimator.