Generalized mixture estimators for the finite population mean

The first order approximation of the theoretical mean square error and assumption of bivariate normality are very often used for the ratio type estimators for the population mean and variance. We have examined the adequacy of the first order approximation and the robustness of various ratio type estimators. We observed that the first order approximation for ratio type mean estimators and ratio type variance estimators works well if the sampling fraction is small and that departure from the assumption of bivariate normality is not a problem for large samples. We have also proposed some generalized mixture estimators which are combinations of the commonly used estimators. We have also extended the proposed generalized mixture estimators to the case when the study variable is sensitive and a non sensitive auxiliary variable is available. We have shown that the proposed generalized mixture estimators are more efficient than other commonly used estimators. An extensive simulation study and numerical examples are also presented

THE EFFICIENT USE OF SUPPLEMENTARY INFORMATION IN FINITE POPULATION SAMPLING

The purpose of writing this book is to suggest some improved estimators using auxiliary information in sampling schemes like simple random sampling, systematic sampling and stratified random sampling. This volume is a collection of five papers, written by nine co-authors (listed in the order of the papers): Rajesh Singh, Mukesh Kumar, Manoj Kr. Chaudhary, Cem Kadilar, Prayas Sharma, Florentin Smarandache, Anil Prajapati, Hemant Verma, and Viplav Kr. Singh. In first paper dual to ratio-cum-product estimator is suggested and its properties are studied. In second paper an exponential ratio-product type estimator in stratified random sampling is proposed and its properties are studied under second order approximation. In third paper some estimators are proposed in two-phase sampling and their properties are studied in the presence of non-response. In fourth chapter a family of median based estimator is proposed in simple random sampling. In fifth paper some difference type estimators are suggested in simple random sampling and stratified random sampling and their properties are studied in presence of measurement error. The authors hope that book will be helpful for the researchers and students who are working in the field of sampling techniques

Computational Approach to Generalized Ratio Type Estimator of Population Mean Under Two Phase Sampling

In the present draft, we propose the computational approach to generalized ratio type estimator of population mean of the main variable under study using auxiliary information. The expressions for the bias and mean square errors (MSE) have been obtained up to the first order of approximation. The minimum value of the MSE of the proposed estimator is also obtained for the optimum value of the characterizing scalar. A comparison has been made with the existing estimators of population mean in two phase sampling. A computing based on numerical example also carried out which shows improvement of proposed estimator over other estimators in two phase sampling as the proposed estimator has lesser mean squared error

A New Estimator based on Auxiliary Information through Quantitative Randomized Response Techniques

An exponential-type estimator is developed for the population mean of the sensitive study variable based on various Randomized Response Techniques (RRT) using a non-sensitive auxiliary variable. The mean squared error (MSE) of the proposed estimator is derived for generalized RRT models. The proposed estimator is compared with competitors in a simulation study and an application. The proposed estimator is found to be more efficient using a non-sensitive auxiliary variable

Exponential Chain Dual to Ratio cum Dual to Product Estimator for Finite Population Mean in Double Sampling Scheme

This paper considers an exponential chain dual to ratio cum dual to product estimator for estimating finite population mean using two auxiliary variables in double sampling scheme when the information on another additional auxiliary variable is available along with the main auxiliary variable. The expressions for bias and mean square error of the asymptotically optimum estimator are identified in two different cases. The optimum value of the first phase and second phase sample size has been obtained for the fixed cost of survey. To illustrate the results, theoretical and empirical studies have also been carried out to judge the merits of the suggested estimator with respect to strategies which utilized the information on two auxiliary variables

Weight Adjustment Methods and Their Impact on Sample-based Inference

Weighting samples is important to reflect not only sample design decisions made at the planning stage, but also practical issues that arise during data collection and cleaning that necessitate weighting adjustments. Adjustments to base weights are used to account for these planned and unplanned eventualities. Often these adjustments lead to variations in the survey weights from the original selection weights (i.e., the weights based solely on the sample units' probabilities of selection). Large variation in survey weights can cause inferential problems for data users. A few extremely large weights in a sample dataset can produce unreasonably large estimates of national- and domain-level estimates and their variances in particular samples, even when the estimators are unbiased over many samples. Design-based and model-based methods have been developed to adjust such extreme weights; both approaches aim to trim weights such that the overall mean square error (MSE) is lowered by decreasing the variance more than increasing the square of the bias. Design-based methods tend to be ad hoc, while Bayesian model-based methods account for population structure but can be computationally demanding. I present three research papers that expand the current weight trimming approaches under the goal of developing a broader framework that connects gaps and improves the existing alternatives. The first paper proposes more in-depth investigations of and extensions to a newly developed method called generalized design-based inference, where we condition on the realized sample and model the survey weight as a function of the response variables. This method has potential for reducing the MSE of a finite population total estimator in certain circumstances. However, there may be instances where the approach is inappropriate, so this paper includes an in-depth examination of the related theory. The second paper incorporates Bayesian prior assumptions into model-assisted penalized estimators to produce a more efficient yet robust calibration-type estimator. I also evaluate existing variance estimators for the proposed estimator. Comparisons to other estimators that are in the literature are also included. In the third paper, I develop summary- and unit-level diagnostic tools that measure the impact of variation of weights and of extreme individual weights on survey-based inference. I propose design effects to summarize the impact of variable weights produced under calibration weighting adjustments under single-stage and cluster sampling. A new diagnostic for identifying influential, individual points is also introduced in the third paper

Generalized Neutrosophic Sampling Strategy for Elevated estimation of Population Mean

One of the disadvantages of the point estimate in survey sampling is that it fluctuates from sample to sample due to sampling error, as the estimator only provides a point value for the parameter under discussion. The neutrosophic approach, pioneered by Florentin Smarandache, is an excellent tool for estimating the parameters under consideration in sampling theory since it yields interval estimates in which the parameter lies with a very high probability. As a result, the neutrosophic technique, which is a generalization of classical approach, is used to deal with ambiguous, indeterminate, and uncertain data. In this investigation, we suggest a new general family of ratio and exponential ratio type estimators for the elevated estimation of neutrosophic population mean of the primary variable utilizing known neutrosophic auxiliary parameters. For the first degree approximation, the bias and Mean Squared Error (MSE) of the suggested estimators are computed. The neutrosophic optimum values of the characterizing constants are determined, as well as the minimum value of the neutrosophic MSE of the suggested estimator is obtained for these optimum values of the characterizing scalars. Because the minimum MSE of the classical estimators of population mean lies inside the estimated interval of the neutrosophic estimators, the neutrosophic estimators are better than the equivalent classical estimators. The empirical investigation, which used both real and simulated data sets, backs up the theoretical findings. For practical utility in various areas of applications, the estimator with the lowest MSE or highest Percentage Relative Efficiency (PRE) is recommended