Sparse regression for extreme values

We study the problem of selecting features associated with extreme values in high dimensional linear regression. Normally, modeling problems, presence abnormal or outliers is considered an anomaly which should either be removed from data remedied using robust regression methods. In many situations, however, are not but rather signals interest; consider traces spiking neurons, volatility finance, events climate science, for example. this paper, we propose a new method sparse high-dimensional motivated by Subbotin, generalized normal distribution, call value model. For our method, utilize ℓp norm loss where p even integer greater than two; demonstrate that increases weight on values. prove consistency and variable selection Lasso penalty, term Extreme Lasso, also analyze theoretical impact observations model parameter estimates concept influence functions. Through simulation studies real-world example, show outperforms other methods currently used literature interest