Estimating a Finite Population Mean Using Transformed Data in Presence of Random Nonresponse

Nelson Kiprono Bii,Christopher Ouma Onyango,John Odhiambo

doi:10.1155/2020/7306315

Nelson Kiprono Bii, Christopher Ouma Onyango + Show 1 more

Open Access

https://doi.org/10.1155/2020/7306315

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Abstract

Developing finite population estimators of parameters such as mean, variance, and asymptotic mean squared error has been one of the core objectives of sample survey theory and practice. Sample survey practitioners need to assess the properties of these estimators so that better ones can be adopted. In survey sampling, the occurrence of nonresponse affects inference and optimality of the estimators of finite population parameters. It introduces bias and may cause samples to deviate from the distributions obtained by the original sampling technique. To compensate for random nonresponse, imputation methods have been proposed by various researchers. However, the asymptotic bias and variance of the finite population mean estimators are still high under this technique. In this paper, transformation of data weighting technique is suggested. The proposed estimator is observed to be asymptotically consistent under mild assumptions. Simulated data show that the estimator proposed is much better than its rival estimators for all the different mean functions simulated.

Highlights

A lot of significance is attached to efficient and cost-effective survey sampling designs in sample surveys while estimating a finite population mean, see for instance [1, 2]
Careful design of samples based on random selection with known probabilities of population elements should be considered
Is gives a target sample of intended respondents where each may provide responses to a set of survey questions that result in an array of responses

Summary

Introduction

A lot of significance is attached to efficient and cost-effective survey sampling designs in sample surveys while estimating a finite population mean, see for instance [1, 2]. As observed in [1], a good sample survey practise and efficient methods of compensating for nonresponse should be adopted. Nonresponse leads to biased results in the estimation of a finite population mean. To minimize the bias and variance resulting from nonresponse, Liang and Zeger [6] noted that it is desirable to incorporate auxiliary data in the process of estimation where the probabilities of response are mostly assumed to be correlated with certain characteristics, for instance, age, race, and income in human population surveys.

Review of Weighting Method

Finite Population Mean Estimator Proposed