Abstract
Abstract The article contains a new technique to estimate the mean of the variate of the interest of the finite population with the help of two auxiliary variates. The technique complies well with the stratified population in which each strata proportion is predicted by taking an initial sample called the first phase sample. When the first phase sample is taken, a second sample is taken from the first sample which is called the second phase sample which is used to estimate the mean of the variate of the interest. In our study, we have considered the population which has two correlated auxiliary variates that pass almost through the origin. In such a situation ratio estimation technique and product estimation technique that provides improved estimates of the mean of the variate of the interest. Our technique considers a ratio-product type exponential estimator of which we have established efficiency theoretically as well as empirically.
Highlights
In sample survey, surveyors use the auxiliary variates in order to increase the accuracy in the estimation of population parameters when the associated variates are readily and inexpensively available to the entire population
This will benefit only if the attainment in precision that is achieved by using the sample auxiliary variate weigh up the loss in precision that has been incurred because of the reduction in the size of the sample for computing mean of the variate of the interest
When information on Xh is unknown Double Stratified Sampling method comes to rescue by using first phase sample to note down value on auxiliary variates
Summary
Surveyors use the auxiliary variates in order to increase the accuracy in the estimation of population parameters when the associated variates are readily and inexpensively available to the entire population. Many times the associated variates are not readily available, in which case, a larger sample is taken provided the collection of information on auxiliary variate is cheap, easy and economical. If the variate of the interest and auxiliary variates are highly correlated the efficiency of the estimators may be increased by using auxiliary variate. Samiuddin and Hanif, 2007, Singh et al, 2011, Sanaulla et al, 2014 and Vishwakarma and Singh, 2015 have used two auxiliary variates for double stratified sampling method. All in all, inspired by their work, a need was felt to propose a new methodology in this area, and the results are discussed in a subsequent section
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