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]