摘要:

Models assuming minimal repair specify that on repair, a failed system is returned to the working state, while the effective age of the system is held constant; that is, the distribution of the time until the next failure of the repaired system is the same as for a system of the same age that has not yet failed. These models are common in the literature of operations research and reliability, and many probabilistic results as well as inferential procedures depend on the minimal repair assumption. We propose two nonparametric tests of the assumption that imperfectly repaired systems are minimally repaired in some models. The large sample theory for these tests is derived from the asymptotic joint distribution of a survival function estimator and the ordinary empirical survival function based on the initial failure times of new or perfectly repaired systems. Simulation results are also provided for the null hypothesis case and under other alternatives.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476470

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

Often when dealing with complex data structures there is no unique way to bootstrap. If the data can be viewed asU1, …,Uniid from some distributionP, then one can bootstrap by resampling theU's. Alternately, one can resample in a more model-based way; that is, by making use of the structure of the modelP. A typical example of this is linear regression, in which the data is (Yi, Xi),i= 1, …,n. One can resample the pairs (Yi, Xi), or one can resample the residuals from a fitted model. This phenomenon arises over quite a wide spectrum of problems, and in many cases the different methods of bootstrapping can give substantially different results. It seems hopeless to come up with a general theory that compares the different ways of bootstrapping. In this article we study in some detail a certain model that arises in reliability theory in which there are two natural ways to bootstrap. This model is described as follows. Available for testing is a sample ofniid systems each having the same structure ofmindependent components. Each system is continuously observed until it fails. For every component in each system, either a failure time or a censoring time is recorded. A failure time is recorded if the component fails before or at the time of system failure; otherwise a censoring time is recorded. Thus the system failure acts as a censoring mechanism on the component lifelengths. In this model bootstrapping can be carried out in two ways: resamplensystems at random from the originalnsystems or formally compute the Kaplan-Meier estimates[Fcirc]1, …,[Fcirc]mof the component life distributionsF1, …,Fm. One then generates artificial lifelengths from these Kaplan-Meier estimates and from those form artificial data. We show that asymptotically, bootstrapping by either method yields correct answers. Intuitively, one expects the model-based method to outperform the other method. The results of an extensive Monte Carlo study show that this is usually true, with substantial gains possible. But there are also some cases when the model-based method does worse than the “naive” model-free method.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476471

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

Viewing the analysis of designed experiments as a model selection problem, we introduce the use of a predictive Bayesian criterion in this context based on the predictive density of a replicate experiment (PDRE). A calibration of the criterion is provided to assist in the model choice. The relationships of the proposed criterion to other prevalent criteria, such as AIC, BIC, and Mallows'sCp, are given. An information theoretic criterion based on the PDRE's of two competing models is also introduced and compared with the usualFstatistic for two nested models. Examples are given to illustrate the proposed methodology.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476472

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

The problem of equivalence assessment of several treatments with a control is considered. The first approach uses a hypothesis testing formulation in which the alternative states global equivalence. With respect to a family of distributions with location parameter, a test based on a two-sided many-one statistic is proposed. Least favorable parameter configuration results are presented as being necessary to evaluate critical values and to determine sample sizes implied by certain power requirements when planning experiments. The second approach concerns a stepwise selection procedure. The goal is to select a subset of treatments containing all those actually equivalent to the control in the absence of global equivalence. The normal case is dealt with in detail for randomized block designs as well as for one-way layouts. Concerning the test problem, optimal allocations of total sample sizes are determined to guarantee specified power requirements for the one-way layout.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476473

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

We consider a class of probit-normal models for binary data and describe ML and REML estimation of variance components for that class as well as best prediction for the realized values of the random effects. ML estimates are calculated using an EM algorithm; for complicated models EM includes a Gibbs step. The computations are illustrated through two examples.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476474

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

We introduce nonparametric versions for many of the hypotheses tested in analysis of variance and repeated measures models, such as the hypotheses of no main effects, no interaction effects, and no factor effects. These natural extensions of the nonparametric hypothesis of equality of thekdistributions in theksample problem have appealing practical interpretations. We concentrate on multivariate repeated measures designs and obtain simple rank statistics for testing these hypotheses. These statistics are the rank transform (RT) versions of the classical statistics for testing hypotheses in repeated measures designs. We emphasize that even though recent research has demonstrated the inappropriateness of the RT method for many parametric hypotheses, the RT procedure is always valid for testing our nonparametric hypotheses. We show that the rank statistics converge in distribution to central chi-squared distributions under their respective nonparametric null hypotheses. The noncentrality parameters under nonparametric contiguous alternatives are obtained. In addition, we present an interpretation of simultaneous confidence intervals and multiple comparison procedures based on rank statistics. Finally, we illustrate the proposed rank tests with a real data set from the statistical literature.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476475

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

The problem of estimating the number of trials in a Binomial distribution is known to be particularly difficult in certain circumstances. Both the maximum likelihood and method-of-moments estimators can produce very erratic results, being extremely sensitive to minor fluctuations in the data. But existing asymptotic theory for these estimators does not provide any insight into this peculiar behavior, as the theory typically produces asymptotic Normal distributions with respectable means and variances. Likewise, the limiting distributions of other estimators do not convey much information about why those estimators might perform better than their more classical counterparts. In this article we develop an alternative asymptotic theory that clearly and vividly depicts not only the erratic performance of the maximum likelihood and method-of-moments estimators, but also the more regular, robust properties of alternative estimators proposed by Carroll and Lombard. We note that the parameter configurations under which these theoretical results are valid are just those exhibited by well-known, “troublesome” data sets. In these settings, the maximum likelihood and method-of-moments estimators have limiting distributions with very heavy tails, such as the Cauchy, whereas the Carroll-Lombard estimators have limiting distributions with very light tails.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476476

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

Analysis of Quantal Response Data.B. J. T. Morgan. London: Chapman and Hall, 1992. xx + 511 pp. $55.

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476477

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476478

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1994.10476480

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor