The Adaptive Design of Experiments and Markovian Models

Abstract

Abstract : Research was conducted in three broad areas: setting confidence intervals following an adaptive or sequential experiment; central limit theory for sums of stationary processes; the monotone change problem and related problems in isotonic inference. For the confidence intervals existing techniques were extended to include grouped sequential methods and to allow for nuisance parameters. The work on central limit theory emphasized state space models (iterated random functions) and non-linear functionals of a linear process In both cases, asymptotic distributions were obtained under very mild continuity conditions on the function or functional that is summed. The central limit theory was used to obtain the limiting distribution of a new test statistic in the context of a change point problem. For this the change point problem was reformulated to allow several gradual changes, as opposed to the single abrupt change implicit in the classical change point problem. The related problems in isotonic inference include a novel suggestion for the appropriate degrees of freedom in an isotonic regression problem.