D. L. McLeish

Hilbert space methods in probability and statistical inference

Hilbert Spaces. Probability Theory. Estimating Functions. Orthogonality and Nuisance Parameters. Martingale Estimating Functions and Projected Likelihood. Stochastic Integration and Product Integrals. Estimating Functions and the Product Integral Likelihood for Continuous Time Stochastic Processes. Hilbert Spaces and Spline Density Estimation. Bibliography. Index.

Sensitivity analysis and the “what if” problem in simulation analysis

We discuss some known and some new results on the score function (SF) approach for simulation analysis. We show that while simulating a single sample path from the underlying system or from an associated system and applying the Radon-Nikodym measure one can: estimate the performance sensitivities (gradient, Hessian etc.) of the underlying system with respect to some parameter (vector of parameters); extrapolate the performance measure for different values of the parameters; evaluate the performance measures of queuing models working in heavy traffic by simulating an associated (auxiliary) queuing model working in light (lighter) traffic; evaluate the performance measures of stochastic models while simulating random vectors (say, by the inverse transform method) from an auxiliary probability density function rather than from the original one (say by the acceptance-rejection method). Applications of the SF approach to a broad variety of stochastic models are given.

A robust alternative to the normal distribution

A wider-tailed family of distributions is suggested as an alternative to the normal distribution having many of the desirable properties of the normal family. One advantage of this alternative is the greater robustness of maximum-likelihood estimates. On suggere une famille de distributions dont les ailes sont plus relevees que celles de la cloche de Gauss, mais qui conservent plusieurs des proprietes les plus attrayantes de la loi normale. On obtient ainsi des estimateurs du maximum de vraisemblance qui sont beaucoup plus robustes.