In the context of a species sampling problem we discuss a non-parametric maximum likelihood estimator for the underlying probability mass function. The estimator is known in the computer science literature as the high profile estimator.... more
In the context of a species sampling problem we discuss a non-parametric maximum likelihood estimator for the underlying probability mass function. The estimator is known in the computer science literature as the high profile estimator. We prove strong consistency and derive the rates of convergence, for an extended model version of the estimator. We also study a sieved estimator for which similar consistency results are derived. Numerical computation of the sieved estimator is of great interest for practical problems, such as forensic DNA analysis, and we present a computational algorithm based on the stochastic approximation of the expectation maximisation algorithm. As an interesting byproduct of the numerical analyses we introduce an algorithm for bounded isotonic regression for which we also prove convergence.
It has often been noticed that, in observing the number of incidents that nurses experience during their shifts, there is a large variation between nurses, and over time. We propose a simple statistical model to describe this phenomenon... more
It has often been noticed that, in observing the number of incidents that nurses experience during their shifts, there is a large variation between nurses, and over time. We propose a simple statistical model to describe this phenomenon and apply this to the Lucia de Berk case. 1
