Optimal estimation of direction in regression models with large number of parameters

We consider the problem of estimating the optimal direction in regression by maximizing the probability that the scalar product between the vector of unknown parameters and the chosen direction is positive. The estimator maximizing this probability is simple in form, and is especially useful for situations where the number of parameters is much larger than the number of observations. We provide examples which show that this estimator is superior to state-of-the-art methods such as the LASSO for estimating the optimal direction