Power transformations to symmetry

Abstract

Power transformations for achieving distributional symmetry are discussed. Estimates of the transformation power are based on general measures of symmetry. They are shown to be consistent and asymptotically normal. Use of the skewness coefficient as a measure of symmetry is shown to be optimal in an important special case. The methods are compared to the likelihood methods of Box & Cox (1964) and alternative methods of Hinkley (1975, 1977). The Box-Cox method or a robust adaptation of it (Carroll, 1980; Bickel & Doksum, 1981) is found to be the generally most suitable method.