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Smearing retransformation

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The Smearing retransformation is used in regression analysis, after estimating the logarithm of a variable. Estimating the logarithm of a variable instead of the variable itself is a common technique to more closely approximate normality. In order to retransform the variable back to level from log, the Smearing retransformation is used.

If the log-transformed variable y is normally distributed with mean

f ( X ) {\displaystyle f(X)} and variance σ 2 {\displaystyle \sigma ^{2}}

then, the expected value of y is given by:

y = exp ( f ( X ) ) exp ( 1 2 σ 2 ) . {\displaystyle y=\exp(f(X))\exp({\frac {1}{2}}\sigma ^{2}).}

References

  1. Duan, Naihua (September 1983). "Smearing Estimate: A Nonparametric Retransformation Method". Journal of the American Statistical Association. 78 (383): 605–610. doi:10.2307/2288126. JSTOR 2288126.
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