On Robust Estimation through the Use of Auxiliary Information by Ratio and Regression Estimators

The ratio and regression estimators that make use of auxiliary information for achieving higher efficiency is applied to education data. Education is critical to our development as individuals and as societies, and it paves the way to a successful and productive future. It provides the potentials for an individual’s intellectual growth and productivity in the society. The objective of this paper is to estimate the ratio of pupils to classroom in Nigeria’s public primary schools as well as to estimate the total pupil population in Nigeria’s public primary schools using the ratio and regression estimators. The data of annual enrolment into public primary schools and the number of classrooms in 2014 were obtained from Universal Basic Education Commission.  Furthermore, the sampling design used is stratified random sampling with equal allocation. Two states were selected from each geo-political zone; making a sample of 12 states The results of the ratio estimator revealed that the estimated national pupil-classroom ratio is approximately 54 and the confidence interval shows that the ratio may lie between the inter 43 and 65 approximately. Similarly, total pupils population is estimated at 20,298,309 and the confidence interval shows that the total population may lie between the inter 16,084,553 to 24,512,065 approximately. The ratio and regression estimators will save time and cost to give reliable estimates. Similarly, using the regression estimator total pupils population is estimated at 20,412,402 and the confidence interval shows that the total population may lie between the inter 16,210,204 to 24,614,600 approximately. Based on this analysis, it is therefore recommended that effort should be intensified to improve the pupil-classroom ratio nationwide and to increase pupils’ enrolment. Key words: Bias, Enrolment, Coefficient of Variation, Confidence interval, Ratio estimation, Regression estimation Robust estimates, Standard error, Variance Abbreviations: EFA - Education for All, UBE - Universal Basic Education, SRS – Simple Random Sample, UNESCO-United Nations Educational, Scientific and Cultural Organizatio

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

A representative sampling plan for auditing health insurance claims

A stratified sampling plan to audit health insurance claims is offered. The stratification is by dollar amount of the claim. The plan is representative in the sense that with high probability for each stratum, the difference in the average dollar amount of the claim in the sample and the average dollar amount in the population, is ``small.'' Several notions of ``small'' are presented. The plan then yields a relatively small total sample size with the property that the overall average dollar amount in the sample is close to the average dollar amount in the population. Three different estimators and corresponding lower confidence bounds for over (under) payments are studied.Comment: Published at http://dx.doi.org/10.1214/074921707000000094 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Coupling methods for multistage sampling

Multistage sampling is commonly used for household surveys when there exists no sampling frame, or when the population is scattered over a wide area. Multistage sampling usually introduces a complex dependence in the selection of the final units, which makes asymptotic results quite difficult to prove. In this work, we consider multistage sampling with simple random without replacement sampling at the first stage, and with an arbitrary sampling design for further stages. We consider coupling methods to link this sampling design to sampling designs where the primary sampling units are selected independently. We first generalize a method introduced by [Magyar Tud. Akad. Mat. Kutat\'{o} Int. K\"{o}zl. 5 (1960) 361-374] to get a coupling with multistage sampling and Bernoulli sampling at the first stage, which leads to a central limit theorem for the Horvitz--Thompson estimator. We then introduce a new coupling method with multistage sampling and simple random with replacement sampling at the first stage. When the first-stage sampling fraction tends to zero, this method is used to prove consistency of a with-replacement bootstrap for simple random without replacement sampling at the first stage, and consistency of bootstrap variance estimators for smooth functions of totals.Comment: Published at http://dx.doi.org/10.1214/15-AOS1348 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org