2 - Tuning of jackknife estimator

Abstract

In this chapter, we introduce the new concept of tuning design weights, which, in turn, leads to a computer friendly tuning methodology. The proposed methodology results in an estimator that is equivalent to the linear regression estimator of the population mean or total. The newly tuned estimation methodology is able to efficiently and effectively estimate the variance of the estimator of the population mean. The estimation of variance of the estimator is a key feature of the proposed newly tuned estimation methodology. In this chapter, we restrict ourselves to the use of a simple random sampling (SRS) scheme. We show that under an SRS scheme, the linear regression estimator is a result of tuning the jackknife sample mean estimator with the chi-squared type distance function. Tuning of the sample jackknife estimator under a dual-to-empirical log-likelihood (dell) function leads to a newly tuned dell-estimator of the population mean. The coverage by the newly tuned estimators, under the chi-square distance and the dell function, is investigated for the Statistical Jumbo Pumpkin Model. The R codes for studying the reliability of the tuned estimators under the chi-squared distance function and the dell function are also provided. Numerical illustrations for both methods are also presented. At the end of the chapter, a few unsolved exercises are given for practice and further investigation. The tuning of a nonresponse in sampling theory is addressed in one of the unsolved exercises. The tuning of a sensitive variable, in the context of estimating the population mean of a sensitive variable, is also introduced through an unsolved exercise. In addition, tuned estimators of geometric mean and harmonic mean are also suggested for further investigation.