Abstract
Nonparametric regression has been widely exploited in survey sampling to construct estimators for the finite population mean and total. It offers greater flexibility with regard to model specification and is therefore applicable to a wide range of problems. A major drawback of estimators constructed under this framework is that they are generally biased due to the boundary problem and therefore require modification at the boundary points. In this study, a bias robust estimator for the finite population mean based on the multiplicative bias reduction technique is proposed. A simulation study is performed to develop the properties of this estimator as well as assess its performance relative to other existing estimators. The asymptotic properties and coverage rates of our proposed estimator are better than those exhibited by the Nadaraya Watson estimator and the ratio estimator.
Highlights
Sample surveys are intended to reduce the time and cost of collecting data while at the same time ensuring valid inference about population quantities
Our focus is to advance the work of Dorfman (1992) who considered a similar problem of estimating the finite population total using nonparametric regression
The results indicate that the multiplicative bias corrected estimator outperforms the usual non-parametric regression estimator proposed by Dorfman (1992) at 95% coverage rate
Summary
Sample surveys are intended to reduce the time and cost of collecting data while at the same time ensuring valid inference about population quantities. Under the model based framework, a super-population model that describes the relationship between the auxiliary variable and the study variable is used to predict the non-sampled values. This has an overall effect of increasing the precision with which population quantities are estimated. Nonparametric regression has been embraced as one of the ways of dealing with the problem of model misspecification In this case, no restrictions are placed on the relationship between the auxiliary variable and the study variable of interest. A major problem that is encountered when using nonparametric kernel based regression over a finite interval such as in the estimation of finite population quantities is the bias at the boundary points. Our focus is to apply a multiplicative bias correction technique to the nonparametric estimation of the finite population mean and to study the asymptotic properties, coverage properties and the conditional properties of the resulting estimate
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