Abstract
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.
Highlights
The main purpose of surveys which are conducted at Local, National and International levels is to gather information and aid public and private sectors in effective policy making [1]
It has been established that the presence of multivariate auxiliary variables, some more robust estimators can be formed by combining up different estimators such as ratio, product or even regression estimators and in each case the individual estimators uses its own random variable [6]
The relationship between each of the variables is linear and positive as indicated in figures 1 and 2. This observation concurs with the existing literature in that the auxiliary variables should be positively correlated with the study variable in question
Summary
The main purpose of surveys which are conducted at Local, National and International levels is to gather information and aid public and private sectors in effective policy making [1]. Researches have proposed estimators that are more efficient in estimating finite population totals using two auxiliary variables [4,5]. Several researchers who have used auxiliary information in the estimation stage of parametric super population models include, Chambers and Danstan [7], Wang and Dorfman [8], Rao et al [9]. The use of auxiliary information in double sampling found out that the proposed estimators did perform better than the mean per unit estimator and compared to the other estimators that don’t utilize the auxiliary information and they are not asymptotically optimum with two auxiliary variables [10]. International Journal of Data Science and Analysis 2018; 4(4): 53-57 information to estimate population total has been investigated as well [11]. Two datasets from the agricultural and environmental sectors were used in order to investigate the properties of the estimator and they gave satisfactory results
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