Robust Estimation of Finite Population Totals Using a Model Based Approach in the Presence of Two Auxiliary Variables
International Journal of Data Science and Analysis
Volume 4, Issue 4, August 2018, Pages: 53-57
Received: Oct. 16, 2018;
Accepted: Oct. 31, 2018;
Published: Nov. 14, 2018
Views 957 Downloads 77
Damaris Felistus Mulwa, 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
Romanus Odhiambo, Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
The utilization of auxiliary information during surveys increases the accuracy of estimators, thereby giving more reliable estimates of the population parameters of interest. It has been established that the presence of more than one auxiliary variables, some more robust estimators can be formed by combining different estimators like product, ratio or even regression estimators and in each case the individual estimators uses its own random variable. One of the most commonly used methods is the ratio method of estimating finite totals which is the foundation of all the other methods that use auxiliary information. In this paper, an estimator of the ratio-exponential class that uses two auxiliary variables has been proposed and its variance derived. After deriving the proposed estimator the coverage probabilities were estimated. Results showed that the interval length of the proposed estimator was narrower and tighter than that of the known Horwitz-Thompson’s estimator. Two datasets from the agricultural and environmental sectors were used in order to investigate the properties of the estimator and they gave satisfactory results. Mean squared error criteria was used to investigate the performance of the proposed estimator and in both cases it had the minimum squared error values. The analysis in these paper is of very great importance in understanding environmental and agricultural data.
Damaris Felistus Mulwa,
George Otieno Orwa,
Robust Estimation of Finite Population Totals Using a Model Based Approach in the Presence of Two Auxiliary Variables, International Journal of Data Science and Analysis.
Vol. 4, No. 4,
2018, pp. 53-57.
Copyright © 2018 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.
S. C and L. S, Estimation in surveys with nonresponse, John Wiley & Sons, 2005.
L. P. S, "Theorie analtytique des probabilities," Courcier, 1820.
K. Cem and C. Hulya, "A new estimator using two auxilary variables," Applied Mathematics and Computation, vol. 162, no. 2, pp. 901-908, 2005.
M. Sachin and J. Singh, "An improved estimator using two auxiliary attributes," Applied Mathematical and Computation, vol. 219, no. 23, pp. 10983-10986, 2013.
K. M, A. O and I. A, "Use of auxiliary variables and asymptotically optimum estimators in double sampling," International Journal of Statistics and Probability, vol. 5, no. 3, 2016.
R. E-H and Z. D, "Estimation of population tota; using local polynomial regression withtwo auxiliary variabkles," Journal of Statistics Application and Probbility, vol. 3, no. 2, 2014.
D. Robson, "Applications of multivariate polykays to the theory of unbiased ratio-type estimation," Journal of the American Statistical Association, vol. 52, no. 280, pp. 511-522, 1957.
M. H. e. a. Hansen, "Some history and reminiscences on survey sampling," Statistical science, vol. 2, no. 2, pp. 180-190, 1987.
S. Bahl and R. Tuteja, "Ratio and Product Type exponential estimators," Journal of Information and Optimization Sciences, vol. 12, no. 1, pp. 159-164, 1991.
J. Lu, Efficient estimator of a finite population mean using two auxiliary variables, biomedical, and power engineering, Mathematical problems in engineering, 2017.
A. H. a. H. P. Dorfman, Estimators of the finite population distribution function using nonparametric regression., The Annals of Statistics, 1993.
R. L. a. D. R. Chambers, "Estimating distribution functions from survey data," Biometrika, vol. 73, no. 3, pp. 597-604, 1986.
W. A. A. M. A. R. a. M. H. A. Abu-Dayyeh, "Some estimators of a finite population mean using auxiliary information.," Applied Mathematics and computation, vol. 139, no. 2, pp. 287-298, 2003.
J. K. J. a. M. H. Rao, "On estimating distribution functions and quantiles from survey data using auxiliary information.," Biometrika, pp. 365-375.
H. P. a. E. M. R. Singh, "Double sampling ratio-product estimator of a finite population mean in sample surveys.," Journal of Applied Statistics, vol. 34, no. 1, pp. 71-85, 2007.