摘要:

When survival data can be divided into natural groups, such as in a clinical trial with patients from a number of different institutions, the question arises whether effects are different for the different groups. For situations where one is concerned with a random pattern of variation over groups, this article proposes testing the null hypothesis of no variation using statistics based on the sums of martingale residuals over subjects within groups. These tests are closely related to the locally most powerful tests of Liang for testing for variation across a large number of strata. The tests are applied to data from a lung cancer trial conducted by the Eastern Cooperative Oncology Group.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476502

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

The methods of optimum experimental design are applied to models in which the variance, as well as the mean, is a parametric function of explanatory variables. Extensions to standard optimality theory lead to designs when the parameters of both the mean and the variance functions, or the parameters of only one function, are of interest. The theory also applies whether the mean and variance are functions of the same variables or of different variables, although the mathematical foundations differ. The example studied is a second-order two-factor response surface for the mean with a parametric nonlinear variance function. The theory is used both for constructing designs and for checking optimality. A major potential for application is to experimental design in off-line quality control.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476503

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

Partial and multiple Bayes factors are introduced to obtain pairwise comparisons of hypotheses in a statistical experiment with a partition on the parameter space. Robust Bayesian analyses are performed by introducing suitable classes of priors and by calculating lower and upper bounds of Bayes factors and posterior probabilities. Classes of intuitively meaningful priors are introduced, including unimodal densities without the constraint of symmetry for the case of precise hypotheses. Procedures for the corresponding optimizations are specified, and examples are given.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476504

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

We present a Bayesian approach for inference and predictions from nonhomogeneous Poisson point processes. The novel feature of our approach is the use of “expert knowledge” or “engineering information” on the mean value function of the process. We describe two scenarios from the field of reliability in which engineering information on the mean value function is available. The first scenario pertains to the prediction of software failures during the debugging phase. Here expert knowledge is provided by the published empirical experiences of software engineers involved with the testing and debugging of several software systems. The second scenario pertains to the prediction of defects in a rail segment for which expert knowledge is supplied by an engineering model.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476505

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

This article develops the multiprocess dynamic Poisson model for estimating and forecasting a Poisson random variable with a timevarying parameter. Its characteristics are similar to the multiprocess dynamic linear model of Harrison and Stevens. Its precision increases when the parameter remains unchanged, it reacts quickly to real parameter changes, and it is not sensitive to outliers. But the observation distribution is Poisson instead of normal, so the gamma conjugate family is used. Perturbation distributions and observation error distributions are not required, because the extrapolated conditional parameter distributions and conditional observations distributions are found directly in the gamma conjugate family. The conditional posterior distribution is found by Bayes's theorem. The theorem of Pena and Guttman about the optimal condensing of the mixture of normal distributions to a single normal distribution in terms of minimizing Kullbeck-Liebler distance is generalized to the optimal condensing of the mixture of twodimensional exponential family members to a single member. The model uses the optimal condensing for the gamma family. Simulation results show that this gives a substantial improvement.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476506

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

Markov chain sampling has recently received considerable attention, in particular in the context of Bayesian computation and maximum likelihood estimation. This article discusses the use of Markov chain splitting, originally developed for the theoretical analysis of general state-space Markov chains, to introduce regeneration into Markov chain samplers. This allows the use of regenerative methods for analyzing the output of these samplers and can provide a useful diagnostic of sampler performance. The approach is applied to several samplers, including certain Metropolis samplers that can be used on their own or in hybrid samplers, and is illustrated in several examples.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476507

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

The observations in parameter-driven models for time series of counts are generated from latent unobservable processes that characterize the correlation structure. These models result in very complex likelihoods, and even the EM algorithm, which is usually well suited for problems of this type, involves high-dimensional integration. In this article we discuss a Monte Carlo EM (MCEM) algorithm that uses a Markov chain sampling technique in the calculation of the expectation in theEstep of the EM algorithm. We propose a stopping criterion for the algorithm and provide rules for selecting the appropriate Monte Carlo sample size. We show that under suitable regularity conditions, an MCEM algorithm will, with high probability, get close to a maximizer of the likelihood of the observed data. We also discuss the asymptotic efficiency of the procedure. We illustrate our Monte Carlo estimation method on a time series involving small counts: the polio incidence time series previously analyzed by Zeger.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476508

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

The Gaussian estimation of a partially nonstationary autoregressive model and the related issue of testing for cointegration using the likelihood ratio test procedure have been considered by others. In this article we extend the Gaussian estimation procedure to partially nonstationary autoregressive moving average models and derive the asymptotic properties of the full-rank and reduced-rank Gaussian estimators. Based on these results, the asymptotic distribution of the likelihood ratio statistic for testing the number of unit roots is obtained. A numerical example based on three U.S. interest rate series is used to illustrate the estimation and testing procedures. The finite-sample properties of the estimation and likelihood ratio test procedures are examined through a small simulation study.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476509

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

We analyze the choice of the truncation lag in the context of the Said-Dickey test for the presence of a unit root in a general autoregressive moving average model. It is shown that a deterministic relationship between the truncation lag and the sample size is dominated by data-dependent rules that take sample information into account. In particular, we study data-dependent rules that are not constrained to satisfy the lower bound condition imposed by Said-Dickey. Akaike's information criterion falls into this category. The analytical properties of the truncation lag selected according to a class of information criteria are compared to those based on sequential testing for the significance of coefficients on additional lags. The asymptotic properties of the unit root test under various methods for selecting the truncation lag are analyzed, and simulations are used to show their distinctive behavior in finite samples. Our results favor methods based on sequential tests over those based on information criteria, because the former show less size distortions and have comparable power.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476510

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

The problems of evaluating and subsequently maximizing the exact likelihood function of vector autoregressive moving average (ARMA) models are considered separately. A new and efficient procedure for evaluating the exact likelihood function is presented. This method puts together a set of useful features that can only be found separately in currently available algorithms. A procedure for maximizing the exact likelihood function, which takes full advantage of the properties offered by the evaluation algorithm, is also considered. Combining these two procedures, a new algorithm for exact maximum likelihood estimation of vector ARMA models is obtained. Comparisons with existing procedures, in terms of both analytical arguments and a numerical example, are given to show that the new estimation algorithm performs at least as well as existing ones, and that relevant real situations occur in which it does better.

ISSN:0162-1459    

DOI:10.1080/01621459.1995.10476511

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor