Robustness of the Simultaneous Estimators of Location and Scale From Approximating a Histogram by a Normal Density Curve

The robust properties of the simultaneous estimators of location and scale parameters (μ*, σ*) proposed by Brown and Hwang are studied. As a pair of simultaneous <italic>M</italic> estimators of location and scale, their asymptotic efficiencies (0.650 for μ* and 0.541 for σ*) are higher than those for median (0.637) and median absolute deviation (0.368) under the normal distribution. Simulation indicates that the distributions of <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="utas_a_663665_o_ilm0001.gif"/> and <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="utas_a_663665_o_ilm0002.gif"/> are much flatter than those based on the sample mean and the sample standard deviation under the normal distribution when the sample size is small.