Yale University
Department of Statistics
Seminar

Wednesday, February 21, 1996

Nicolas Hengartner

Department of Statistics
Yale University

Let X_1,...,X_n be an i.i.d. sample from a Poisson mixture distribution p(k) = \int_0^\infty s^k e^{-s}f(s) ds/k!. Rates of convergence in Integrated Mean Squared error of orthogonal series estimators for the mixing density f are studied. We derive upper and lower bounds on the IMSE and show, and conclude that our estimator achieves the optimal rate of convergence of order (log n log log n)^r. The analysis further reveals that the considered estimator is automatically adaptive. The analysis of the lower bound is of particular interest: previous analysis have shown that there was a gap between the lower and upper bounds. My analysis eliminates this. It also is applicable to general mixtures of discrete random variables.

Seminar to be held in Room 107, 24 Hillhouse @ 12:15 pm