SUMMARY It is well known that Bartlett adjustment reduces level-error of the likelihood ratio statistic from order n-l to order n3/2. In the present note we show that level-error of the adjusted statistic is actually order n2.

On the level-error after Bartlett adjustment of the likelihood ratio statistic

http://www2.cirano.qc.ca/~dufourj/Web_Site/Dufour_Khalaf_1998_MCTCompanion_W.pdf

Monte Carlo Test Methods in Econometrics

A system (machine) is observed to operate in 1 of 2 modes. The most common mode is loaded (or regular) operation. Occasionally the system is placed in an unloaded state, wherein while the system is mechanically still operating, it is assumed that the failure intensity is lower due to this reduction in operating intensity. A proportional hazards framework is used to capture this potential reduction in failure intensity due to switching of operating modes. In either operating condition, analyzed maintenance-records indicate that the system was occasionally shut down, and either a minor or a major repair was undertaken. Furthermore, despite such repairs, it is observed that both modes of operation (loaded or unloaded) resulted in random failures. On failure, 1 of 3 actions are taken: (1) failures were minimally repaired, (2) given a minor repair, or (3) given a major repair. Both minor and major repairs are assumed to impact the intensity following a virtual age process of the general form proposed by Kijima. This research develops a statistical model of such an operating/maintenance environment. Its purpose is to quantify the impacts of performing these repair actions on the failure intensities. Field data from an industrial-setting demonstrate that appropriate parameter estimates for such multiple phenomena can be obtained. Providing a richer, more detailed, modeling of the failure intensity of a system incorporating both operating conditions and repair effects has important ramifications for maintenance planning. This paper refers to related research, in which optimal timing of maintenance repairs depends fundamentally on the failure rate of the system.

A general repair, proportional-hazards, framework to model complex repairable systems

http://www.cirano.qc.ca/pdf/publications/2000s-15.pdf

Simulation based finite and large sample tests in multivariate regressions

Many applications of Amari's dual geometries involve one or more submanifolds imbedded in a supermanifold. In the differential geometry literature, there is a set of equations that describe relationships between invariant quantities on the submanifold and supermanifold when the Riemannian connection is used. We extend these equations to statistical manifolds, manifolds on which a pair of dual connections is defined. The invariant quantities found in these equations include the mean curvature and the statistical curvature which are used in statistical calculations involving such topics as information loss and efficiency. As an application of one of these equations, the Bartlett correction is interpreted in terms of curvatures and other invariant quantities.

/pdf/fundamental-equations-for-statistical-submanifolds-with-46ghtqp5mg.pdf

Fundamental equations for statistical submanifolds with applications to the bartlett correction

SUMMARY We describe, for the numerical calculation of Bartlett adjustments, a method which may be of use when the cumulants of the log likelihood derivatives are easy to determine in one parametrization while the hypotheses to be tested are all linear in some other parametrization. The method relies on the cartesian tensorial nature of those cumulants and should be particularly convenient in connection with statistical packages with structure similar to GLIM.

P. Blaesild

Papers

A note on the calculation of Bartlett adjustments