Predictive estimation of population mean in two-phase sampling

ABSTRACT

The present investigation deals with the problem of estimation of population mean in two-phase sampling. In the presence of two auxiliary variables, some classes of estimators have been proposed through predictive approach. Properties of the proposed classes of estimators have been studied, and the unbiased versions of these estimators along with their approximate variance expressions are obtained under simple random sampling without replacement scheme. The respective optimum strategies of the proposed estimators are discussed, and their empirical and graphical comparisons with some contemporary estimators of population mean have been made. Suitable recommendations to the survey practitioner are given.     

An improved alternative estimation procedure for current population mean in presence of positively and negatively correlated auxiliary variables in two-occasion rotation patterns

Abstract

The present study confirms the influential role of a positively and a negatively correlated auxiliary variables in enhancing the precision of estimates of current population mean in two occasion rotation (successive) sampling. Exponential-type estimators of current population mean have been proposed for three different situations: (i) the information on a positively correlated auxiliary variable is readily available on both occasions (ii) the information on a negatively correlated auxiliary variable is readily available on both occasions and (iii) the information on both positively and negatively correlated auxiliary variables are readily available on both the occasions. The characteristics of the proposed estimators have been explored and their efficacious performances are compared with the natural and recent contemporary estimators. Optimum replacement strategies of the proposed estimation procedures have been formulated. Simulation and empirical studies are carried out to justify the proposition of the proposed estimators and appropriate recommendations have been put forward to the survey practitioners.     

A simulation study: estimation of population mean using two auxiliary variables in stratified random sampling

ABSTRACT

This paper deals with the problem of estimating the finite population mean in stratified random sampling by using two auxiliary variables. This paper proposed a ratio-cum-product exponential type estimator of population mean under different situations: (i) when there is presence of non-response and measurement errors on the study as well as auxiliary variables; (ii) when there is non-response on the study and auxiliary variables but with no measurement error; (iii) when there is complete response on study variable but there is presence of non-response and measurement error on the auxiliary variables and (iv) when there are complete response and measurement error on study as well as auxiliary variables. The expressions of the bias and mean square error of the proposed estimator have been obtained up to the first degree of approximation. The proposed estimator has been compared with usual unbiased estimator, ratio estimator and other existing estimators and the conditions obtained to show the efficacy of the proposed estimator over other considered estimators. Simulation study is carried out to support the theoretical findings.     

Some estimation procedures using a linear model in successive sampling

ABSTRACT

In successive sampling some recent works depict the use of super-population models where information on stable auxiliary variable over occasions has been utilized. Stability character of auxiliary variable may not sustain, if the duration between occasions is large. To cope with such situations, the present work is an attempt to develop some estimation procedures by utilizing the information on two independent auxiliary variables through a linear super-population model. Some estimators are proposed to estimate the current population mean in two occasions successive (rotation) sampling. Optimum replacement strategies are formulated and performances of the proposed estimators have been discussed. Results are interpreted through empirical studies.     

Some calibration estimators for finite population mean in two-stage stratified random sampling

Abstract

In the present article, an effort has been made to develop calibration estimators of the population mean under two-stage stratified random sampling design when auxiliary information is available at primary stage unit (psu) level. The properties of the developed estimators are derived in-terms of design based approximate variance and approximate consistent design based estimator of the variance. Some simulation studies have been conducted to investigate the relative performance of calibration estimator over the usual estimator of the population mean without using auxiliary information in two-stage stratified random sampling. Proposed calibration estimators have outperformed the usual estimator without using auxiliary information.     

Estimation of finite population variance in successive sampling using multi-auxiliary variables

ABSTRACT

In this paper, a general class of estimators for estimating the finite population variance in successive sampling on two occasions using multi-auxiliary variables has been proposed. The expression of variance has also been derived. Further, it has been shown that the proposed general class of estimators is more efficient than the usual variance estimator and the class of variance estimators proposed by Singh et al. (2011) when we used more than one auxiliary variable. In addition, we support this with the aid of numerical illustration.     

Estimation of population distribution function involving measurement error in the presence of non response

Abstract

This article addresses the problem of estimating population distribution function for simple random sampling in the presence of non response and measurement error together. We suggest a general class of estimators for estimating the cumulative distribution function using the auxiliary information. The expressions for the bias and mean squared error are derived up to the first order of approximation. The performance of the proposed class of estimators is compared with considered estimators both theoretically and numerically. A real data set is used to support the theoretical findings.     

Point estimation using tail modelling for right skew populations

ABSTRACT

We evaluate the merits of estimators for right-skewed data which are motivated by a distributional assumption for the tail of the population. Our aim is to make a coherent account of estimators of this type already existing in the literature as well as suggesting some modifications, and to compare their performance empirically to other conceivable alternatives. Our results indicate that making use of parametric models to derive the explicit form of estimators can be a fruitful approach for a wide range of right-skewed populations when auxiliary data is not available, especially for small samples.     

Preliminary test estimators in double sampling with two auxiliary variables

An attempt has been mads to suggest some estimators for population mean in double sampling with two auxiliary variables., alternative to the usual regression estimator. When the experimenter has partial Information about the mean of the auxiliary variable or variables, preliminary test estimators can be used. The bias, mean square error, relative efficiency and optimum allocation of sample sizes are obtained for the suggested estimators.     

Calibration Approach-based Product Estimator of Finite Population Total with Subsampling of Nonrespondents under Single and Two-phase Sampling

Hansen and Hurwitz (1946) technique–based estimator of population total is proposed using the calibration approach under the assumption that the auxiliary variable is negatively correlated with the study variable. The variance estimation is also considered. The two-phase sampling case is also explored. The theoretical results are demonstrated through empirical studies using both generated and real population data. The proposed estimator of population total outperforms the existing estimators in terms of the criteria of relative bias and relative root mean square error.     

Inference on the Common Variance of Correlated Normal Random Variables

ABSTRACT

Scale equivariant estimators of the common variance σ², of correlated normal random variables, have mean squared errors (MSE) which depend on the unknown correlations. For this reason, a scale equivariant estimator of σ² which uniformly minimizes the MSE does not exist. For the equi-correlated case, we have developed three equivariant estimators of σ²: a Bayesian estimator for invariant prior as well as two non-Bayesian estimators. We then generalized these three estimators for the case of several variables with multiple unknown correlations. In addition, we developed a system of confidence intervals which produce the desired coverage probability while being efficient in terms of expected length.     

Improved estimator of population total in PPS sampling

In this paper, we have considered an estimation of the population total Y of the study variable y, making use of information on an auxiliary variable x. A class of estimators for the population total Y using transformation on both the variables study as well as auxiliary has been suggested based on the probability proportional to size with replacement (PPSWR). In addition to many the usual PPS estimator, Reddy and Rao's (1977) estimator and Srivenkataramana and Tracy's (1979, 1984, 1986) estimators are shown to be members of the proposed class of estimators. The variance of the proposed class of estimators has been obtained. In particular, the properties of 75 estimators based on different known population parameters of the study as well as auxiliary variables have been derived from the proposed class of estimators. In support of the present study, numerical illustrations are given.     

Estimation of rare and clustered population variance in adaptive cluster sampling

Abstract

Many researchers used auxiliary information together with survey variable to improve the efficiency of population parameters like mean, variance, total and proportion. Ratio and regression estimation are the most commonly used methods that utilized auxiliary information in different ways to get the maximum benefits in the form of high precision of the estimators. Thompson first introduced the concept of Adaptive cluster sampling, which is an appropriate technique for collecting the samples from rare and clustered populations. In this article, a generalized exponential type estimator is proposed and its properties have been studied for the estimation of rare and highly clustered population variance using single auxiliary information. A numerical study is carried out on a real and artificial population to judge the performance of the proposed estimator over the competing estimators. It is shown that the proposed generalized exponential type estimator is more efficient than the adaptive and non adaptive estimators under conventional sampling design.     

Exponential-Type Estimators of the Mean of a Sensitive Variable in the Presence of Nonsensitive Auxiliary Information

Sousa et al. and Gupta et al. suggested ratio and regression-type estimators of the mean of a sensitive variable using nonsensitive auxiliary variable. This article proposes exponential-type estimators using one and two auxiliary variables to improve the efficiency of mean estimator based on a randomized response technique. The expressions for the mean squared errors (MSEs) and bias, up to first-order approximation, have been obtained. It is shown that the proposed exponential-type estimators are more efficient than the existing estimators. The gain in efficiency over the existing estimators has also been shown with a simulation study and by using real data.     

Estimation of population mean based on dual use of auxiliary information in non response

Whenever there is auxiliary information available in any form, the researchers want to utilize it in the method of estimation to obtain the most efficient estimator. When there exists enough amount of correlation between the study and the auxiliary variables, and parallel to these associations, the ranks of the auxiliary variables are also correlated with the study variable, which can be used a valuable device for enhancing the precision of an estimator accordingly. This article addresses the problem of estimating the finite population mean that utilizes the complementary information in the presence of (i) the auxiliary variable and (ii) the ranks of the auxiliary variable for non response. We suggest an improved estimator for estimating the finite population mean using the auxiliary information in the presence of non response. Expressions for bias and mean squared error of considered estimators are derived up to the first order of approximation. The performance of estimators is compared theoretically and numerically. A numerical study is carried out to evaluate the performances of estimators. It is observed that the proposed estimator is more efficient than the usual sample mean and the regression estimators, and some other families of ratio and exponential type of estimators.     

A Class of Estimators Using Auxiliary Information for Estimating Finite Population Variance in Presence of Measurement Errors

This article addresses the problem of estimating the population variance using auxiliary information in the presence of measurement errors. When the measurement error variance associated with study variable is known, a class of estimators of the population variance using auxiliary information has been proposed. We obtain the bias and mean squared errors of the suggested class of estimators upto the terms of order n ^?1, and also optimum estimators in asymptotic sense of the class with approximate mean squared error formula.     

Alternative mean-squared error estimators for synthetic estimators of domain means

In forest management surveys, the mean of a variable of interest (Y) in a population composed of N equal area spatial compact elements is increasingly estimated from a model linking Y to an auxiliary vector X known for all elements in the population. It is also desired to have synthetic estimates of the mean of Y in spatially compact domains (forest stands) with no or at most one sample-based observation of Y. We develop three alternative estimators of mean-squared errors (MSE) that reduce the risk of a serious underestimation of the uncertainty in a synthetic estimate of a domain mean in cases where the employed model does not accounts for domain effects nor spatial autocorrelation in unobserved residual errors. Expansions of the estimators including anticipated effects of a spatial autocorrelation in residual errors are also provided. Simulation results indicate that the conventional model-dependent (MD) population-level estimator of variance in a synthetic estimate of a domain mean underestimates uncertainty by a wide margin. Our alternative estimators mitigated, in settings with weak to moderate domain effects and relatively small sample sizes, to a large extent, the problem of underestimating uncertainty. We demonstrate applications with examples from two actual forest inventories.     

Optimal estimation for finite population mean in two-phase sampling

Using two-phase sampling scheme, we propose a general class of estimators for finite population mean. This class depends on the sample means and variances of two auxiliary variables. The minimum variance bound for any estimator in the class is provided (up to terms of ordern ⁻¹). It is also proved that there exists at least a chain regression type estimator which reaches this minimum. Finally, it is shown that other proposed estimators can reach the minimum variance bound, i.e. the optimal estimator is not unique.     

Use of multiauxiliary variables to cope with non response in estimation of current population mean in two-occasion successive sampling

ABSTRACT

The present work utilizes the information on multiauxiliary variables to neutralize the negative effect of non response in estimation of current population mean in two-occasion successive sampling. Generalized exponential type estimators have been proposed for the situation when non response occurs at both occasion or at first occasion or at current (second) occasion in two-occasion successive sampling. Properties of the proposed estimators have studied and empirical studies are carried out to justify the preposition of estimators. Suitable recommendations have been made.