Archive




Volume 9, Issue 4, July 2020, Page: 101-105
Exploring Data-Reflection Technique in Nonparametric Regression Estimation of Finite Population Total: An Empirical Study
Langat Reuben Cheruiyot, Department of Mathematics and Computer Sciences, School of Science & Technology, University of Kabianga, Kericho, Kenya
Received: May 6, 2020;       Accepted: May 25, 2020;       Published: Jun. 3, 2020
DOI: 10.11648/j.ajtas.20200904.13      View  54      Downloads  36
Abstract
In survey sampling statisticians often make estimation of population parameters. This can be done using a number of the available approaches which include design-based, model-based, model-assisted or randomization-assisted model based approach. In this paper regression estimation under model based approach has been studied. In regression estimation, researchers can opt to use parametric or nonparametric estimation technique. Because of the challenges that one can encounter as a result of model misspecification in the parametric type of regression, the nonparametric regression has become popular especially in the recent past. This paper explores this type of regression estimation. Kernel estimation usually forms an integral part in this type of regression. There are a number of functions available for such a use. The goal of this study is to compare the performance of the different nonparametric regression estimators (the finite population total estimator due Dorfman (1992), the proposed finite population total estimator that incorporates reflection technique in modifying the kernel smoother), the ratio estimator and the design-based Horvitz-Thompson estimator. To achieve this, data was simulated using a number of commonly used models. From this data the assessment of the estimators mentioned above has been done using the conditional biases. Confidence intervals have also been constructed with a view to determining the better estimator of those studied. The findings indicate that proposed estimator of finite population total that is nonparametric and uses data reflection technique is better in the context of the analysis done.
Keywords
Conditional Biases, Reflection Technique, Confidence Lengths, Nonparametric Regression Estimation
To cite this article
Langat Reuben Cheruiyot, Exploring Data-Reflection Technique in Nonparametric Regression Estimation of Finite Population Total: An Empirical Study, American Journal of Theoretical and Applied Statistics. Vol. 9, No. 4, 2020, pp. 101-105. doi: 10.11648/j.ajtas.20200904.13
Copyright
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
Alberts T and Karunamuni R. J. (2007). Boundary correction methods in Kernel density estimation. Presentation slides downloaded from internet.
[2]
Albers M. G. (2011). Boundary Estimation of Densities with Bounded Support. Swiss Federal Institute of Technology Zurich. Masters’ Thesis.
[3]
Breidt, B. F. and Opsomer, J. D. (2000). Local Polynomial regression in Survey Sampling. Annals of Statistics 28 (August): 1026-1053.
[4]
Breidt, F. J. and Opsomer, J. (2009). Nonparametric and Semiparametric Estimation in Complex Surveys, Handbooks of Statistics, vol. 29B, eds. D. Pfeffermann and C. R. Rao, 103-121.
[5]
Brewer (2002). Combined survey sampling inference: weighing Basu’s Elephants. London, Arnold a member of the Hodder Headline Group.
[6]
Čížek, P., & Sadıkoglu, S. (2020). Robust nonparametric regression: A review. Retrieved from https://doi.org/10.1002/wics.1492.
[7]
Cochran, W. G. (1977), Sampling Techniques (3rd ed.), New York: John Wiley.
[8]
Cox B. G. (1995) Business survey methods. New York: John Wiley.
[9]
Dhekale, B. S., Sahu, P. K., Vishwajith, K. P., Mishra, P., & Narsimhaiah, L. (2017). Application of parametric and nonparametric regression models for area, production and productivity trends of tea (Camellia sinensis) in India. Indian Journal of Ecology, 44 (2), 192-200.
[10]
Dorfman, A. H.(1992), Nonparametric Regression for Estimating Totals in Finite Populations. In proceedings of the section on Survey Research Methods. Alexandria VA: American Statistics Association. Pp 622-625.
[11]
Eubank, R. L., 1988. Spline Smoothing and Nonparametric Regression. Marcel Dekker, New York.
[12]
Eubank, R. L., Speackman, P. L., (1991). A bias reduction theorem with application in nonparametric regression, Scandinavian Journal of Statistics. 18, 211- 222.
[13]
Gasser, Th., Miiller, H. G., (1979). In: Gasser, Th., Rosenblatt, M. (Eds.) Kernel estimation of regression functions: in Smoothing Techniques for Curve Estimation. Springer, Heidelberg, pp. 23-68.
[14]
Horvitz, D. G. and Thompson, D. J. (1952). A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association, 47, 663-685.
[15]
Kyung-Joon C. and Schucany W. R. (1998), Nonparametric kernel regression estimation near endpoints Journal of Statistical Planning and Inference 66 289-304.
[16]
Rice, J., 1984. Boundary modification for kernel regression. Communication in Statistics. A 13, 893-900.
[17]
Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis, London: Chapman and Hall.
[18]
Schuster E. F (1985). Incorporating support into nonparametric estimators of densities, Communication in Statistics. A 14, 1123-36.
[19]
Tibshirani, R., & Wasserman, L. (2015). Nonparametric Regression- Statistical Machine Learning. Retrieved May 22, 2020, from http://www.stat.cmu.edu.
Browse journals by subject