| A new thresholding method, based on L-statistics and called order thresholding, is proposed as a technique for improving the power when testing against high-dimensional alternatives. The new method allows great flexibility in the choice of the threshold parameter. This results in improved power over the soft and hard thresholding methods. Moreover, order thresholding is not restricted to the normal distribution. An extension of the basic order threshold statistic to high-dimensional ANOVA is presented. Furthermore, the application of order thresholding to Pearson's chi-square test is developed. The performance of the basic order threshold statistic and its extensions is evaluated with extensive simulations. |
