Speed of convergence for estimators of finite translation mixture distributions
G. S. Dissanayake, Frits H. Ruymgaart · Journal of nonparametric statistics · 2000
A suitably tapered Fourier transform is used to obtain a simple and explicit construction of estimators for the c.d.f.'s of finite translation mixtures. An a.s. speed of L 1-convergence is derived for these c.d.f.'s which corroborates the lower bound for such rates recently derived in Chen (1995) for arbitrary mixtures. In the translation case the rates are determined by the tail behavior of theFourier transform of the kernel of the given location family, i.e., by the degree of ill-posedness of the mixture problem.