Boundary Bias Correction Using Weighting Method in Presence of Nonresponse in Two-Stage Cluster Sampling

Abstract

Kernel density estimators due to boundary effects are often not consistent when estimating a density near a finite endpoint of the support of the density to be estimated. To address this, researchers have proposed the application of an optimal bandwidth to balance the bias-variance trade-off in estimation of a finite population mean. This, however, does not eliminate the boundary bias. In this paper weighting method of compensating for nonresponse is proposed. Asymptotic properties of the proposed estimator of the population mean are derived. Under mild assumptions, the estimator is shown to be asymptotically consistent.

Estimation of a Finite Population Mean under Random Nonresponse Using Kernel Weights

“…Generally, it is noted from Table 3 that the mean squared error values for the proposed estimator are relatively smaller than the rest of the estimators considered. e transformation of data method estimator due to [13] follows closely in the second place with smaller mean squared error values compared to nonparametric regression-based estimator due to [14]. From this comparison of the mean squared error values, it can be concluded that the proposed estimator is more efficient than the other two estimators considered.…”

“…e results are given in Table 4. From the values obtained, it is noted that the confidence interval lengths for the proposed estimator are much tighter than those of the estimators due to [13,14]. Hence, at 95% level of confidence, the estimator proposed in this study performs better than its rival estimators.…”

“…Negative values of the bias imply underestimation while positive values of the bias indicate overestimation of the finite population mean by the different estimators. e proposed estimator has relatively smaller values of the bias followed by transformation of data method estimator due to [13].…”

“…e values of the bias, mean squared error, and confidence interval lengths are given in the following tables. Note that Y INW is the estimator of the finite population mean proposed in this study and Y TDM is the transformation of data method estimator of the finite population mean due to [13] whereas Y REG is the nonparametric regression estimator due to [14]. Both Y TDM and Y REG were used for comparative purposes with the proposed estimator.…”

“…A simulation experiment was conducted using R code in order to compare the performance of the proposed estimator in two-stage cluster sampling with the transformed estimator due to [13] and the nonparametric regression estimator due to [14]. An asymptotic framework is used where both the population number of clusters and the sample number of clusters are large.…”