Random thresholds for linear model selection

A method is introduced to estimate the number of significant coefficients in non ordered model selection problems. The method is based on a convenient random centering of the partial sums of the ordered observations. Based on $L-$statistics methods we show consistency of the proposed estimator. An extension to unknown parametric distributions is considered. The method is then applied to a regression model and interpreted as a random threshold procedure. Simulated examples are included to show the accuracy of the estimator.