Conditional Frequentist Sequential Tests for the Drift of Brownian Motion
نویسنده
چکیده
In this paper, we consider the problem of sequentially testing simple hypotheses concerning the drift of a Brownian motion process from a unified Bayesian and frequentist perspective. The conditional frequentist approach to testing statistical hypotheses has been utilized in a variety of settings to produce tests that are virtually equivalent to their objective Bayesian counterparts. Herein, we show that, at least for standard classes of stopping boundaries, the unified theory developed so far does not directly apply to the problem at hand. We thus motivate the need for a new conditioning strategy that ensures the existence of a conditional frequentist test whose answer essentially matches the objective Bayesian test. Under a quite general set of assumptions, we show that the new form of conditioning can still be interpreted as conditioning on the evidence present in the data as represented by P -values. Further properties of the resulting procedure, including ancillarity of the partition associated to the conditioning statistic and the characterization of the no-decision region, are studied in detail in the setting of the familiar sequential probability ratio test. ∗Research was supported by the U.S. National Science Foundation, Grants DMS-0073952 at the National Institute of Statistical Sciences, DMS-0103265, and the Statistical and Applied Mathematical Sciences Institute. This research formed part of the author’s Ph.D. thesis at Duke University, where he was supported by a Ph.D. Fellowship awarded by Fundação para a Ciência e a Tecnologia, Portugal, with reference PRAXIS XXI/BD/15703/98.
منابع مشابه
On the Bias of Estimation of a Brownian Motion Drift following Group Sequential Tests
Group sequential tests have been widely used to control the type I error rate at a prespecified level in comparative clinical trials. It is well known that due to the optional sampling effect, conventional maximum likelihood estimates will exaggerate the treatment difference, and hence a bias is introduced. We consider a group sequentially monitored Brownian motion process. An analytical expres...
متن کاملEffects of heat generation/absorption on natural convection of nanofluids over the vertical plate embedded in a porous medium using drift-flux model
In this paper, natural convection heat transfer over a vertical plate in a Darcy porous medium saturated with a nanofluid subject to heat generation/absorption was theoretically studied. The governing partial differential equations were transformed to a set of ordinary differential equations using similarity transformations and solved using finite difference method. The influence of parametric ...
متن کاملAn Invariant Sequential Test for Zero Drift Based on the First Passage T ! Mes in Brownian Motion
متن کامل
Sequential tests and estimates after overrunning based on p - value combination
Often in sequential trials additional data become available after a stopping boundary has been reached. A method of incorporating such information from overrunning is developed, based on the “adding weighted Zs” method of combining p-values. This yields a combined p-value for the primary test and a median-unbiased estimate and confidence bounds for the parameter under test. When the amount of o...
متن کاملSequential Estimation for Fractional Ornstein-Uhlenbeck Type Process
We investigate the asymptotic properties of the sequential maximum likelihhod estimator of the drift parameter for fractional Ornstein-Uhlenbeck type process satisfying a linear stochastic differential equation driven by fractional Brownian motion.
متن کامل