Extending Product Method of Estimation to Positive Correlation Case in Surveys

The product method of estimation (Murthy, 1964) complements the ratio method when the study variate, y, and an auxiliary variate, x, have negative correlation. However, such cases are not frequent in survey practice. This paper suggests a simple transformation of x in the more common situation of positive correlation between y and x, to permit a product method of estimation rather than a ratio method. This leads to the advantage that the bias and mean square error have exact expressions. The technique developed by Quenouille (1956) and applied by Shukla (1976) is used for making the estimator unbiased. The minimum variance situation is investigated. Two numerical examples are included. The case of negative correlation is also examined.