Ratio-type exponential estimator for the population mean at the current occasion in the presence of non-response in successive sampling (Q2061772)

The paper deals with sampling over two occasions. On the first occasion a simple random sample of size $n$ is drawn from the population. On the second occasion, $m$ units are retained from the first sample and the remaining $(n-m)$ units are drawn afresh from the population keeping the sample size $n$ fixed. It is of interest to estimate the population mean on the second occasion. Further, the authors assume that nonresponse occurs only on the second (current) occasion. They present a good review of the several estimators in the literature along with their MSE $s$. Next they consider a ratio type estimator utilising the available auxiliary information. However, they concentrate on exponentiation of the ratio estimator and denote their choice by $t$. The motivation for such a choice could have been specified. Using this estimator $t$, they minimise its MSE and consider $t(\text{opt.})$. In the next step, the authors take a linear combination of $t(\text{opt.})$ and another purposively chosen estimator. Denote this by $e$. For comparison by illustration, an empirical example at the end is given to show that $t$ is better than the other chosen estimators.