Abstract
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.
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Acknowledgement
We first met in 1968 when you spoke at a session I chaired at an IMS Regional Meeting in Madison. From our regular contacts since that time, I have become very impressed with your major contributions in the areas of nonparametric and semi-parametric inference. May you continue to make important contributions for a long time to come. (R.J.)
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Yeo, IK., Johnson, R. (2014). An Empirical Characteristic Function Approach to Selecting a Transformation to Symmetry. In: Lahiri, S., Schick, A., SenGupta, A., Sriram, T. (eds) Contemporary Developments in Statistical Theory. Springer Proceedings in Mathematics & Statistics, vol 68. Springer, Cham. https://doi.org/10.1007/978-3-319-02651-0_11
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DOI: https://doi.org/10.1007/978-3-319-02651-0_11
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