What is a sound methodology to improve the efficiency of the regression coefficients when we are interested in predicting the larger values of the marginal distribution (tails)?
For example, we want to predict seismic waves based on a number of covariates recorded by our probes. Data can not be assumed to be strictly linear, given that most earthquakes develop abruptly after a certain covariates threshold is reached. The vast majority of observations are not considered harmful and should be down-weighted in our analysis. What we are really interested in estimating are the more extreme outcomes.
[thoughts...] Weighted least square comes to mind, but how should the weights be calculated? Is quantile regression with, say, $\tau = [0.2, 0,8]$ a better approach? [/thoughts]