Smearing retransformation explained

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 \sigma ^{2}

then, the expected value of y is given by:

y = \exp(f(X))\exp( (1)/(2) \sigma ^{2).} ^[1]

Notes and References

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