Control variate selection for Monte Carlo integration

Monte Carlo integration with variance reduction by means of control variates can be implemented the ordinary least squares estimator for intercept in a multiple linear regression model integrand as response and covariates. Even without special knowledge on integrand, significant efficiency gains obtained if variate space is sufficiently large. Incorporating large number procedure may however result (i) certain instability (ii) possibly prohibitive computation time. Regularizing preselecting appropriate via Lasso turns out to increase accuracy additional computational cost. The findings numerical experiment are confirmed concentration inequalities error.