Estimating a finite population mean under random non response in two stage cluster sampling with replacement

Journal of Probability and Statistics

2019

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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.

Section: Methods Of Reducing Boundary Bias Due To Nadaraya-watson Estmentioning

confidence: 99%

Section: Proposed Estimator Of Finite Population Mean Using Modified mentioning

confidence: 99%

“…. Consider the Nadaraya-Watson estimator given by (4.4) in [1]. In addition, consider (, ) for ∈ [0, 1) where = so that for = ( − )/ one can obtain…”

Section: Asymptotic Bias Of the Proposed Estimatormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Journal of Probability and Statistics

2019

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“…Many authors such as [1][2][3][4] have looked at estimation of a finite population mean in the presence of nonresponse using various assumptions. However, the estimators developed in these studies need improvements on the efficiency and the bias.…”

Section: Introductionmentioning

confidence: 99%

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

Journal of Probability and Statistics

2020

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Nonresponse is a potential source of errors in sample surveys. It introduces bias and large variance in the estimation of finite population parameters. Regression models have been recognized as one of the techniques of reducing bias and variance due to random nonresponse using auxiliary data. In this study, it is assumed that random nonresponse occurs in the survey variable in the second stage of cluster sampling, assuming full auxiliary information is available throughout. Auxiliary information is used at the estimation stage via a regression model to address the problem of random nonresponse. In particular, auxiliary information is used via an improved Nadaraya–Watson kernel regression technique to compensate for random nonresponse. The asymptotic bias and mean squared error of the estimator proposed are derived. Besides, a simulation study conducted indicates that the proposed estimator has smaller values of the bias and smaller mean squared error values compared to existing estimators of a finite population mean. The proposed estimator is also shown to have tighter confidence interval lengths at 95% coverage rate. The results obtained in this study are useful for instance in choosing efficient estimators of a finite population mean in demographic sample surveys.

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

International Journal of Mathematics and Mathematical Sciences

2020

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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.