Smearing retransformation

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

$f(X)$ and variance $\backslash sigma^2$

then, the expected value of y is given by:

$y\; =\; \backslash exp(f(X))\backslash exp(\backslash frac\{1\}\{2\}\backslash sigma^2).$ {{cite journal |last1=Duan |first1=Naihua |date=September 1983 |title=Smearing Estimate: A Nonparametric Retransformation Method |journal=Journal of the American Statistical Association |volume=78 |issue=383 |pages=605–610 |doi=10.2307/2288126|jstor=2288126 }}