Living beyond Our Means

As someone who has been advocating “living beyond one’s means” since before the Reagan administration, I welcome Thomas’s endorsement of the idea. If we embrace the maxim that statistics is about variation then we should stand ready to explore how that variation varies with covariates. Assuming, as theory may tempt us to do, that covariates shift only the central tendency of the response, while variation around the central tendency remains unperturbed is rarely plausible. Signal plus iid noise is a dangerous fiction. Nonparametric regression methods have encouraged us to think much more flexibly about how covariate effects vary over x-space, slicing design space into segments that each deserve their own local estimate. Quantile regression seeks to do something similar, slicing the range of the response variable into local conditional quantile functions. Combining the two approaches by estimating nonparametric conditional quantile functions offers a flexible way of characterizing the entire conditional distribution of Y |X. While I find myself completely in accord with the ends set forth in “Beyond,” I cannot condone many of the means employed to achieve them. While not descending to the depths of the Cheneyesque – rendition, black ops, waterboarding – there is an element of (data) torture that risks undermining the whole enterprise. I’ll begin by explaining some of my reservations about parametric alternatives and their Bayesian elaborations for nonparametric quantile regression. To conclude there will be some malicious comments about expectiles.