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

Calibration Estimation for Ratio Estimators in Stratified Sampling for Proportion Allocation

Calibration has established itself as an important methodological instrument in large scale production of statistics. In this paper, we propose calibration estimation for ratio estimator in stratified sampling and derive the estimator of the variance of the calibration estimation ratio estimator in stratified sampling in case proportion allocation

Parameter estimation in the presence of auxiliary information

Dissertação para obtenção do Grau de Doutora em Estatística e Gestão de Risco, Especialidade em EstatísticaIn survey research, there are many situations when the primary variable of interest is sensitive. The sensitivity of some queries can give rise to a refusal to answer or to false answers given intentionally. Survey can be conducted in a variety of settings, in part dictated by the mode of data collection, and these settings can differ in how much privacy they offer the respondent. The estimates obtained from a direct survey on sensitive questions would be subject to high bias. A variety of techniques have been used to improve reporting by increasing the privacy of the respondents. The Randomized Response Technique (RRT), introduced byWarner in 1965, develops a random relation between the individual’s response and the question. This technique provides confidentiality to respondents and still allows the interviewers to estimate the characteristic of interest at an aggregate level. In this thesis we propose some estimators to improve the mean estimation of a sensitive variable based on a RRT by making use of available non-sensitive auxiliary information. In the first part of this thesis we present the ratio and the regression estimators as well as some generalizations in order to study the gain in the estimation over the ordinary RRT mean estimator. In chapters 4 and 5 we study the performance of some exponential type estimators, also based on a RRT. The final part of the thesis illustrates an approach to mean estimation in stratified sampling. This study confirms some previous results for a different sample design. An extensive simulation study and an application to a real dataset are done for all the study estimators to evaluate their performance. In the last chapter we present a general discussion referring to the main results and conclusions as well as showing an application to a real dataset which compares the performance of study estimators

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

Improved Modified Ratio Estimation of Population Mean Using Information on Size of the Sample

In sample surveys, auxiliary information is used for estimation to improve the efficiency of estimators. Increased precision can be obtained when the variable under study is highly correlated with auxiliary information. In this study, the sample size has been used as information for improved estimation of population mean of the main variable under study. A new modified generalized ratio type estimator of population mean has been proposed and the efficiency was examined using Murthy (1967) and Mukhopadhyay (2009) dataset. The large sample properties, the bias and the mean squared error of the newly proposed modified ratio estimator were obtained up to first order of approximation. The optimum value of the characterizing scalar which minimizes the mean squared error was obtained and the minimum value of the mean squared error of the proposed modified ratio estimator for this optimum value was also obtained. A theoretical comparison of the proposed modified ratio estimators was made with the other existing related estimators of population mean using auxiliary information. The conditions under which the proposed modified ratio estimators perform better than the other existing estimators of population mean are given. A numerical study was also carried out to see the performances of the proposed modified ratio estimators and some existing related ratio estimators of population mean and verify the conditions under which the proposed modified ratio estimators are better than some other existing related ratio estimators considered. It was shown that the proposed modified ratio estimators perform better than some existing related ratio estimators as they are having lower mean squared errors. Keywords: Ratio Estimator, Sample size, Bias, Mean Squared Error, Efficienc

Modified ratio-product estimator of population mean in the presence of median and coefficient of variation of the auxiliary variable in stratified random sampling

For the past decades, the estimation of population mean is one of the challenging aspects in sampling survey techniques and much effort has been employed to improve the precision of estimates. In this research work, we proposed a modified ratio-product estimator of population mean of the variable of interest using median and coefficient of variation of the auxiliary variable in stratified random sampling scheme. The expression of bias and MSE of the proposed estimator have been obtained under large sample approximation, asymptotically optimum estimator (AOE) is identified with its approximate MSE formula. Estimator based on “estimated optimum values” was also investigated. Theoretical and empirical comparison of proposed estimator with some other ratio and product estimator justified the performance of the proposed estimator. There is a minimum of 15 percent reduction in the MSE from each of the existing ratio and product estimators considered. Thus most preferred over the existing estimators for the use in practical application.Keywords: bias, mean square error, auxiliary variable, optimum estimator, stratified random sampling, study variabl

Generalized Ratio-cum-Product Estimator for Finite Population Mean under Two-Phase Sampling Scheme

A method to lower the MSE of a proposed estimator relative to the MSE of the linear regression estimator under two-phase sampling scheme is developed. Estimators are developed to estimate the mean of the variate under study with the help of auxiliary variate (which are unknown but it can be accessed conveniently and economically). The mean square errors equations are obtained for the proposed estimators. In addition, optimal sample sizes are obtained under the given cost function. The comparison study has been done to set up conditions for which developed estimators are more effective than other estimators with novelty. The empirical study is also performed to supplement the claim that the developed estimators are more efficient

A Simple Random Sampling Modified Dual to Product Estimator for estimating Population Mean Using Order Statistics

Bandopadhyaya (1980) developed a dual to product estimator using robust modified maximum likelihood estimators (MMLE’s). Their properties were obtained theoretically and supported through simulations studies with generated as well as one real data set. Robustness properties in the presence of outliers and confidence intervals were studied

Exponential Type Product Estimator for Finite Population Mean with Information on Auxiliary Attribute

The main objective of the present study is to develop a new modified unbiased exponential type product estimator for the estimation of the population mean. The proposed estimator possesses the characteristic of a bi-serial negative correlation between the study variable and its auxiliary attribute. Efficiency comparison has been carried out between the proposed estimator and the existing estimators theoretically and numerically