Estimators with continuous and discrete parameters

We consider estimation problems where some of the parameters come from a continuous set, such as the set of real numbers, and other parameters come from a discrete set, such as the set of integers. Some specific applications where estimators of this type arise are considered: direction estimation, period estimation from sparse observations, and noncoherent detection of communications signals. In each case we derive the asymptotic statistical properties of the estimators, and develop fast algorithms for their computation. Concepts from the geometry of numbers and techniques for the analysis empirical processes are involved.
Robby McKilliam is a post doc at the Institute for Telecommunications Research at the University of South Australia, Adelaide. His fields of interest are number theory, estimation theory, statistical signal processing and communications. He admires Lamport's structured proofs and is a fan of reproducible research. In December 2010 he completed his PhD at the University of Queensland, Brisbane, Australia. In 2006 he completed his undergraduate studies in computer systems engineering and mathematics at the University of Queensland. Robby's recreational interests are: swimming, skiing, math, motorbikes, videogames, wine, beer and coffee.