The Lambert Way to Gaussianize Heavy-Tailed Data with the Inverse of Tukey’s h Transformation as a Special Case

Table 2

In each subtable: (first rows) average, (middle rows) proportion of estimates below truth, and (bottom rows) empirical standard deviation times . True and .

(a) Truly Gaussian data:

Median

Gaussian MLE

IGMM

Lambert MLE

NA

Ratio

(b) No fourth moments:

Median

Gaussian MLE

IGMM

Lambert MLE

NA

Ratio

NA

NA

NA

NA

(c) Non-existing mean:

	Median	Gaussian MLE		IGMM				Lambert MLE				NA
												Ratio
50
100
1000
50
100
1000
50							NA				NA
100							NA				NA
1000							NA				NA

(d) Extreme heavy tails:

	Median	Gaussian MLE		IGMM				Lambert MLE				NA
												Ratio
50
100
1000
50
100
1000
50							NA				NA
100							NA				NA
1000							NA				NA