On Improvement in Estimating Population Parameter(s) Using Auxiliary Information

The purpose of writing this book is to suggest some improved estimators using auxiliary information in sampling schemes like simple random sampling and systematic sampling. This volume is a collection of five papers. The following problems have been discussed in the book: In chapter one an estimator in systematic sampling using auxiliary information is studied in the presence of non-response. In second chapter some improved estimators are suggested using auxiliary information. In third chapter some improved ratio-type estimators are suggested and their properties are studied under second order of approximation. In chapter four and five some estimators are proposed for estimating unknown population parameter(s) and their properties are studied. This book will be helpful for the researchers and students who are working in the field of finite population estimation.Comment: 63 pages, 8 tables. Educational Publishing & Journal of Matter Regularity (Beijing

Nonparametric Additive Model-assisted Estimation for Survey Data

An additive model-assisted nonparametric method is investigated to estimate the finite population totals of massive survey data with the aid of auxiliary information. A class of estimators is proposed to improve the precision of the well known Horvitz-Thompson estimators by combining the spline and local polynomial smoothing methods. These estimators are calibrated, asymptotically design-unbiased, consistent, normal and robust in the sense of asymptotically attaining the Godambe-Joshi lower bound to the anticipated variance. A consistent model selection procedure is further developed to select the significant auxiliary variables. The proposed method is sufficiently fast to analyze large survey data of high dimension within seconds. The performance of the proposed method is assessed empirically via simulation studies

A simple variance estimator of change for rotating repeated surveys: an application to the EU-SILC household surveys

A common problem is to compare two cross-sectional estimates for the same study variable taken on two different waves or occasions, and to judge whether the change observed is statistically significant. This involves the estimation of the sampling variance of the estimator of change. The estimation of this variance would be relatively straightforward if cross-sectional estimates were based on the same sample. Unfortunately, samples are not completely overlapping, because of rotations used in repeated surveys. We propose a simple approach based on a multivariate (general) linear regression model. The variance estimator proposed is not a model-based estimator. We show that the estimator proposed is design consistent when the sampling fractions are negligible. It can accommodate stratified and two-stage sampling designs. The main advantage of the approach proposed is its simplicity and flexibility. It can be applied to a wide class of sampling designs and can be implemented with standard statistical regression techniques. Because of its flexibility, the approach proposed is well suited for the estimation of variance for the European Union Statistics on Income and Living Conditions surveys. It allows us to use a common approach for variance estimation for the different types of design. The approach proposed is a useful tool, because it involves only modelling skills and requires limited knowledge of survey sampling theory

Small Area Shrinkage Estimation

The need for small area estimates is increasingly felt in both the public and private sectors in order to formulate their strategic plans. It is now widely recognized that direct small area survey estimates are highly unreliable owing to large standard errors and coefficients of variation. The reason behind this is that a survey is usually designed to achieve a specified level of accuracy at a higher level of geography than that of small areas. Lack of additional resources makes it almost imperative to use the same data to produce small area estimates. For example, if a survey is designed to estimate per capita income for a state, the same survey data need to be used to produce similar estimates for counties, subcounties and census divisions within that state. Thus, by necessity, small area estimation needs explicit, or at least implicit, use of models to link these areas. Improved small area estimates are found by "borrowing strength" from similar neighboring areas.Comment: Published in at http://dx.doi.org/10.1214/11-STS374 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

On Improved Estimation of Population Mean using Qualitative Auxiliary Information

This paper deals with the estimation of population mean of the variable under study by improved ratio-product type exponential estimator using qualitative auxiliary information. The expression for the bias and mean squared error (MSE) of the proposed estimators has been derived to the first order of approximation. A comparative approach has been adopted to study the efficiency of proposed and previous estimators. The present estimators provide us significant improvement over previous estimators leading to the better perspective of application in various applied areas. The numerical demonstration has been presented to elucidate the novelty of paper. Keywords: Exponential estimator, auxiliary attribute, Proportion, bias, mean squared error, efficiency. Mathematics Subject Classification 2010: 62D0