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An Empirical Characteristic Function Approach to Selecting a Transformation to Symmetry

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Contemporary Developments in Statistical Theory

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 68))

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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.)

Author information

Authors and Affiliations

  1. Department of Statistics, Sookmyung women’s University, Seoul 140-742, Seoul, Korea

    In-Kwon Yeo

  2. Department of Statistics, University of Wisconsin-Madison, 53706, Madison, WI, USA

    Richard A. Johnson

Authors
  1. In-Kwon Yeo
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  2. Richard A. Johnson
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Corresponding author

Correspondence to In-Kwon Yeo .

Editor information

Editors and Affiliations

  1. North Carolina State Universy, Raleigh, North Carolina, USA

    Soumendra Lahiri

  2. Department of Mathematical Sciences, Binghampton University, Binghamton, New York, USA

    Anton Schick

  3. Applied Statistics Unit, Kolkata, India

    Ashis SenGupta

  4. Department of Statistics, University of Georgia, Athens, Georgia, USA

    T.N. Sriram

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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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