Title: On estimation of the amount of sparsity in normal mixture models
Authors: Natalia A Stepanova - Carleton University (Canada) [presenting]
Yibo Wang - Univeristy of Alberta (Canada)
Abstract: The motivation comes from a variable selection problem in sparse normal mixtures. For this problem, the sharp selection boundaries, that is, the necessary and sufficient conditions for the possibility of successful variable selection in the exact and almost full regimes are available. The existing selection boundaries, as well as the procedure that provides almost full selection, depend on the fraction of nonzero means, which is generally unknown. We present a new estimator for the fraction of nonzero means in normal mixture models with relatively few nonzero means that are only moderately large. We show that, in the region where variable selection is possible, the new estimator dominates (in terms of the minimax rate of convergence) the existing estimators proposed earlier in similar contexts; the same conclusion continues to hold for the region where signal detection is possible. Moreover, our estimator nearly attains the optimal rate of convergence. The obtained analytical results are illustrated numerically.