### 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