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I largely agree with what you are saying but estimating the population transformation that makes the transformed data Gaussian from a finite sample is far from
by srean 10y ago
I largely agree with what you are saying but estimating the population transformation that makes the transformed data Gaussian from a finite sample is far from trivial.
If you have any pointers to results that show distribution free guarantee of increased power I would be super happy to read.
Here's a question for you , why not just deal with the quantiles directly (for example with quantile regression for regression tasks) and not map it to the quantiles of a Gaussian ?
- apathy 10y agoquantile regression is computationally intensive and inverse transformations usually less so. Although you could certainly make the case that, given enough data, quantile regression better captures what we actually want to find, most of the time (i.e. how's this effect diverge towards the extremes). Normit typically (not sure if universally) has the lovely property of giving you something like a marginal t-test without the assumptions of mixture-of-gaussians errors. You don't jerk around with U-statistics and thus the sample size doesn't make the test statistics so damned granular.
- srean 10y agoThanks for responding, we are definitely in agreement. I have used both, in my experience quantile regression seems better behaved at the tail than quantile transformation in regression tasks. I think if one can make the transform conditional on the covariate they would be comparable.