Abstract
New estimators for estimating the finite population mean using two auxiliary variables under simple and stratified sampling design is proposed. Their properties (e.g., mean square error) are studied to the first order of approximation. More so, some estimators are shown to be a particular member of this estimator. Furthermore, comparison of the proposed estimator with the usual unbiased estimator and other estimators considered in this paper reveals interesting results. These results are further supported with an empirical study using four natural data from literature.
Highlights
In real life, the problem of the estimation of population parameters like mean, proportion, variance, and ratio of two population means are common in virtually all discipline and facet of life
When information is available on the auxiliary variable that is positively correlated with the study variable, the ratio method of estimation proposed by Cochran (1940) is a suitable estimator to estimate the population mean and when the correlation is negative the product method of estimation as envisaged by Robson (1957) and Murthy (1964) is appropriate
Under simple random sampling without replacements (SRSWOR), the suggested estimator as demonstrated through the theory and empirical results is always better than estimators considered in this study when one of the auxiliary variate is positively correlated with the study variate, the other is negatively correlated with the study variable and the two are negatively correlated with each other
Summary
The problem of the estimation of population parameters like mean, proportion, variance, and ratio of two population means are common in virtually all discipline and facet of life. An agriculturist might be interested in the total yield of maize taking into consideration the fertilizer levels, soil type, number of workers in a specific plot, regions etc The use of this type of variables (known as auxiliary information in sample survey design) results in efficient estimate of population parameters (e.g. mean) under some realistic conditions. In this situation, Olkin (1958) was the first author to deal with the problem of estimating the mean of a survey variable when auxiliary variables are made available He suggested the use of information on more than one supplementary characteristic, positively correlated with the study variable, considering a linear combination of ratio estimators based on each auxiliary variable separately. Motivated by Srivenkataramana (1980), Bandyopadhyay (1980) and Singh et al (2005) and with the aim of providing a more efficient estimator; we propose, in this paper, a new estimator for Y when two auxiliary variables are available under simple and stratified sampling design
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