Abstract If the variates x and y are linearly related by a regression through the origin and if the population mean for the variate x is known, then a ratio estimator such as is generally more efficient than the sample mean as an estimator of the population mean . The efficiency of ratio type estimation can sometimes be improved if the correlated variates x and y can be expressed as the sum of k corresponding components, x = x 1 + ··· + x k and y = y 1 + ··· + y k . When the individual components x 1 and y i are more highly correlated than x and y, a componentwise ratio estimator such as is generally more efficient than . This increased efficiency is retained when such estimators are adjusted to eliminate bias.