An empirical characteristic function approach to selecting a transformation to symmetry

초록

Somewhat surprisingly, the empirical characteristic function can provide the basis for selecting a transformation to achieve near symmetry. In this chapter, we propose to estimate the transformation parameter by minimizing a weighted squared distance between the empirical characteristic function of transformed data and the characteristic function of a symmetric distribution. Asymptotic properties are established when a random sample is selected from an unknown distribution. We also consider the selection of weight functions that yield a closed form for the distance function. A small Monte Carlo simulation shows transforming data by our method lead to more symmetry than those by the maximum likelihood method when the population has heavy tails.