Estimation of tuber weight using ratio estimator based on ranked set sampling

Ranked Set Sampling (RSS) was first proposed by McIntyre (1952) [1] to enhance the efficiency of the population mean. In statistical inferences, the estimation of population parameters using information obtained from a sample is an important method. This involves choosing an appropriate sampling method to collect the data. RSS is an efficient sampling method used for data collection [2]. It is a cost-effective sampling technique when the variable of interest is expensive or difficult to measure, but it could be ranked easily at a negligible cost. Under equal allocation, RSS performs better than simple random sampling (SRS). The performance of RSS further improves when appropriate unequal allocation is used instead of equal allocation. RSS presumes that the sampling units are correctly ranked with respect to variable of interest either before or after its quantification. This is called perfect ranking scenario, but this may not be possible always while dealing with real life situations. In these situations, one could take help of some other characteristics for ranking, which is supposed to be inexpensive, easily available, and highly correlated with the main characteristic of interest. Unlike perfect ranking scenario, the ranking so obtained may be referred to as a concomitant ranking because of its dependence on a concomitant variable. In the terminology of classical sampling, this characteristic is known as an auxiliary variable [3]. 
Here, on the availability of concomitant variables, ratio estimation based on ranked set sampling is proposed. In the present paper, ratio estimator of the population mean based on RSS is suggested, and it is shown that the ratio estimator based on RSS is more efficient than the estimators based on SRS. These procedures are illustrated using a real data set regarding the yield of tuber (potato). The technique is more useful to those who look for cost-effective sampling technique for estimating agricultural products that are grown underground, such as potatoes, ginger, turmeric, garlic, onions, beetroot, peanuts, etc.