Asymptotic normality in mixture models
Sara van de Geer · ESAIM Probability and Statistics · 1997
We study the estimation of a linear function 0 = R adF 0 of a distribution F 0 , using i.i.d.observations of the mixture p F 0 = R k( y )dF 0 (y).Let Fn be the maximum likelihood estimator of F 0 and ^ n = R ad Fn .W e examine the asymptotic distribution of ^ n .A problem here is that usually, Fn does not dominate F 0 .Our main a i m i s t o s h o w that this can be overcome by considering the convex combination Fn + ( 1 ; )F 0 , with < 1.