Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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An Empirical Characteristic Function Approach to Selecting a Transformation to Normality

  • Yeo, In-Kwon (Department of Statistics, Sookmyung Women's University) ;
  • Johnson, Richard A. (Department of Statistics, University of Wisconsin-Madison) ;
  • Deng, XinWei (Department of Statistics, Virginia Tech)
  • Received : 2014.11.29
  • Accepted : 2014.04.29
  • Published : 2014.05.31
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Abstract

In this paper, we study the problem of transforming to normality. 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 the normal distribution. Our approach also allows for other symmetric target characteristic functions. Asymptotics are established for a random sample selected from an unknown distribution. The proofs show that the weight function $t^{-2}$ needs to be modified to have thinner tails. We also propose the method to compute the influence function for M-equation taking the form of U-statistics. The influence function calculations and a small Monte Carlo simulation show that our estimates are less sensitive to a few outliers than the maximum likelihood estimates.

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References

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