RATES OF CONVERGENCE FOR THE GAUSSIAN MIXTURE SIEVE

摘要: Gaussian mixtures provide a convenient method of densityestimation that lies somewhere between parametric models and kernel densityestimators. When the number components mixture is allowed to increase as sample size increases, model called sieve. We establish bound on rate convergence in Hellinger distance for using sieve assuming true density itself Gaussians; underlying mixing measure densityis not necessarilyassumed have finite support. Computing involves some delicate calculations since sieve—as measured bybracketing entropy—and saturation rate, cannot be found standard methods. has compact support, kn ∼ n 2/3 /� log n� 1/3 yields order � 1+η� /6/n1/6 every η> 0� The rates depend heavilyon tail behavior density. sensitivity diminished byusing robust which includes long-tailed component