"To within" as a phrase, means this. The statistic (or any mathematical value) shows us something. The mathematical value is a statistic which shows a tendencies. There is therefore, a scale of value. Normally, such scales can be reflected by Place Value.
It is common to see decimal values of Tenths, Hundredths, and Thousandths.
So, where the precision or accuracy is concerned, the phrase "to within" refers to the degree of accuracy. So sentences are written this way:
The machine could cut the steel to within a Tenth of an Millimeter...
(or) Hundredth of a Millimeter (or) a Ten Thousandth of a Millimeter.
Your statistical data might be referred to this way in your sentence:
"...the statistic is APPROXIMATES a scale factor the square of the third moment."
(I hope that helps)