Estimation for a scale parameter with known coefficient of variation

A loss function proposed by Wasan (1970) is well-fitted for a measure of inaccuracy for an estimator of a scale parameter of a distribution defined onR+=(0, ∞). We refer to this loss function as the K-loss function. A relationship between the K-loss and squared error loss functions is discussed. And an optimal estimator for a scale parameter with known coefficient of variation under the K-loss function is presented.