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

AUXILIARY INFORMATION AND A PRIORI VALUES IN CONSTRUCTION OF IMPROVED ESTIMATORS

This volume is a collection of six papers on the use of auxiliary information and a priori values in construction of improved estimators. The work included here will be of immense application for researchers and students who employ auxiliary information in any form. Below we discuss each paper: 1. Ratio estimators in simple random sampling using information on auxiliary attribute. Prior knowledge about population mean along with coefficient of variation of the population of an auxiliary variable is known to be very useful particularly when the ratio, product and regression estimators are used for estimation of population mean of a variable of interest. However, the fact that the known population proportion of an attribute also provides similar type of information has not drawn as much attention. In fact, such prior knowledge can also be very useful when a relation between the presence (or absence) of an attribute and the value of a variable, known as point biserial correlation, is observed. Taking into consideration the point biserial correlation between a variable and an attribute, Naik and Gupta (1996) defined ratio, product and regression estimators of population mean when the prior information of population proportion of units, possessing the same attribute is available. In the present paper, some ratio estimators for estimating the population mean of the variable under study, which make use of information regarding the population proportion possessing certain attribute are proposed. The expressions of bias and mean squared error (MSE) have been obtained. The results obtained have been illustrated numerically by taking some empirical populations considered in the literature

Applications of statistical methods and techniques to auditing and accounting

Statistical Methods;Auditing;accounting/ accountancy

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

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

On the estimation of population variance using auxiliary attribute in absence and presence of non-response

In this article we proposed a new class of estimators for estimating thefinite population variance using available auxiliary attribute in absence and presence of non-response problem. Properties such as bias and mean square error of the proposed class are derived up to the first order of approximation. The proposed class is more efficient than the Singh et al. (1988), Shabbir and Gupta (2007), Singh and Solanki (2013a), usual sample variance and regression estimators

Inference and learning in sparse systems with multiple states

We discuss how inference can be performed when data are sampled from the non-ergodic phase of systems with multiple attractors. We take as model system the finite connectivity Hopfield model in the memory phase and suggest a cavity method approach to reconstruct the couplings when the data are separately sampled from few attractor states. We also show how the inference results can be converted into a learning protocol for neural networks in which patterns are presented through weak external fields. The protocol is simple and fully local, and is able to store patterns with a finite overlap with the input patterns without ever reaching a spin glass phase where all memories are lost.Comment: 15 pages, 10 figures, to be published in Phys. Rev.