A Multiplicative Bias Corrected Nonparametric Estimator for a Finite Population Mean
American Journal of Theoretical and Applied Statistics
Volume 5, Issue 5, September 2016, Pages: 317-325
Received: Sep. 28, 2015;
Accepted: Oct. 20, 2015;
Published: Sep. 28, 2016
Views 3716 Downloads 134
Bonface Miya Malenje, Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Winnie Onsongo Mokeira, Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Romanus Odhiambo, Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
George Otieno Orwa, Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
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.
Bonface Miya Malenje,
Winnie Onsongo Mokeira,
George Otieno Orwa,
A Multiplicative Bias Corrected Nonparametric Estimator for a Finite Population Mean, American Journal of Theoretical and Applied Statistics.
Vol. 5, No. 5,
2016, pp. 317-325.
A. H. Dorfman. (1992). Nonparametric regression for estimating totals in finite pop- ulations, proceedings of the section on survey research methods. American Statistical Association, 1992, pp. 622-625.
Breidt, F. J., & Opsomer, J. D. (2000, 08). Local polynomial regression estimators in survey sampling. Ann. Statist., 28 (4), 1026– 1053.
Chambers, R., & Dorfman, A. (2003). Robust sample survey inference via boot- strapping and bias correction: The case of the ratio estimator.
Chambers, R. L., Dorfman, A. H., & Wehrly, T. E. (1993). Bias robust estimation in finite populations using nonparametric calibration. Journal of the American Statistical Association, 88 (421), 268-277. Cochran, W. G. (2007). Sampling techniques. John Wiley & Sons.
Efron, B. (1982). the jackknife, the bootstrap and other resampling plans. Society for Industrial and Applied Mathematics.
Fan, J., & Gijbels, I. (1992, 12).Variable bandwidth and local linear regression smoothers Ann. Statist., 20 (4), 2008–2036.
Gasser, T., & Müller, H.-G. (1979). Kernel estimation of regression functions.
Godambe, V. (1955). A unified theory of sampling from finite populations. Journal of the Royal Statistical Society. Series B (Methodological), 269–278.
Hengartner, N., Matzner-Lober, E., Rouviere, L., & Burr, T. (2009). Multiplicative bias corrected nonparametric smoothers.
Kwong-Aquino, A. A. H. (2011). Nonparametric model-based predictive estimation in survey sampling. The Philippine Statistician.
Linton, O., & Nielsen, J. P. (1994). A multiplicative bias reduction method for nonparametric regression. Statistics & Probability Letters, 19 (3), 181–187.
Onyango, C. O., Otieno, R. O., & Orwa, G. O. (2010). Generalised model based confidence intervals in two stage cluster sampling. Pakistan Journal of Statistics and Operation Research, 6 (2), 101–115.
Ouma, C., & Wafula, C. (2007). Bootstrap confidence intervals for model-based surveys. East African Journal of Statistics, 1 (1), 84–90.
Pensky, M., Vidakovic, B., et al. (1999). Adaptive wavelet estimator for nonparametric density deconvolution. The Annals of Statistics, 27 (6), 2033–2053.
Priestley, M., & Chao, M. (1972). Non-parametric function fitting. Journal of the Royal Statistical Society. Series B (Methodological), 385–392.
Rao, J. N., & Wu, C. (1988). Resampling inference with complex survey data.
Rueda, M., & Sánchez-Borrego, I. (2009). A predictive estimator of finite population mean using nonparametric regression. Computational Statistics, 24 (1), 1–14.
Zheng, H., & Little, R. (2004). Inference for the population total from probability-proportional-to-size samples based on predictions from a penalized spline non- parametric model. Journal of Official statistics.
Zheng, H., & Little, R. J. (2003). Penalized spline model-based estimation of the finite populations total from probability-proportional-to-size samples. Journal of offi statistics-Stockholm-, 19 (2), 99–118.