摘要:

A collection ofIsimilar items generates point event histories; for example, machines experience failures or operators make mistakes. Suppose the intervals between events are modeled as iid exponential (λi, or the counts as Poisson (λiti,) for the ith item. Furthermore, so as to represent between-item variability, each individual rate parameter, λi, is presumed drawn from a fixed (super) population with densitygλ(·; θ), θ being a vector parameter: a parametric empirical Bayes (PEB) setup. Forgλ, specified alternatively as log-Studentt(n) or gamma, we exhibit the results of numerical procedures for estimating superpopulation parameters ll and for describing pooled estimates of the individual rates, λi, obtained via Bayes's formula. Three data sets are analyzed, and convenient explicit approximate formulas are furnished for λiestimates. In the Student-tcase, the individual estimates are seen to have a robust quality.

ISSN:0040-1706    

DOI:10.1080/00401706.1987.10488178

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

Experimental data are presented for which the Student-tdistribution provides a plausible model. A grouped maximum likelihood estimation approach is developed. A data set is presented that is accurately modeled by a distribution with tails heavier than a Cauchy distribution.

ISSN:0040-1706    

DOI:10.1080/00401706.1987.10488179

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

Tanner and Wang (in press) have introduced the data augmentation algorithm for the analysis of parametric missing data problems. In this article, this paradigm is used to develop an algorithm for the nonparametric estimation of the hazard function from grouped and censored lifetime data. This algorithm makes use of the notions of cross-validation and multiple imputation to prescribe the appropriate degree of smoothing for the nonparametric hazard estimate. A procedure for estimating the variance of the estimator is also proposed. The nonparametric hazard estimate and corresponding variance formula are shown to perform well in a simulation study. The algorithm is illustrated with a numerical example.

ISSN:0040-1706    

DOI:10.1080/00401706.1987.10488180

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

Methods of approximate conditional inference in location and scale parameter distributions, based on normal approximations to the distributions of signed square roots of likelihood ratio statistics, are discussed. These methods are applied to obtain approximate inference for the quantiles and scale parameter of the log generalized gamma distribution from uncensored samples, assuming that the index parameter of the distribution is known. As special cases, approximate inference in the extreme value and normal distributions from Type II censored samples is considered. The accuracy of the approximate methods for small samples is illustrated by comparison with exact results in some examples.

ISSN:0040-1706    

DOI:10.1080/00401706.1987.10488181

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

Inferences on the parameters in a two-parameter exponential lifetime model when the data are Type I censored are limited to asymptotic approximations or to conditional constructions around the observed number of lifetimes. The asymptotic methods are simple to implement when constructing confidence regions on the scale and guarantee time parameters of the model. Their small sample properties have not been previously explored, however. This study provides Monte Carlo results to evaluate these properties. For univariate inference on the scale parameter, convergence of the coverage probabilities to nominal levels is slow until the sample size reaches 25. For the guarantee time parameter, two asymptotically equivalent procedures behave similarly, anF-distribution-based method performing slightly better for smaller sample sizes. In addition, a simultaneous confidence region and confidence bands on the survivor function are constructed from the univariate intervals. Their performance mimics that of the single intervals on the scale parameter, suggesting caution in application when the sample size is small.

ISSN:0040-1706    

DOI:10.1080/00401706.1987.10488182

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

Failures of solid-state electronic components are often caused by manufacturing defects. Typically, a small proportion of the manufactured components has one or more defects that cannot be detected in a simple inspection but that will eventually cause the component to fail. If a component has no such defects, the probability that it will fail under carefully controlled conditions is virtually 0. By assuming a time-to-failure distribution for the units that are susceptible to failure from manufacturing defects, laboratory life tests of limited duration can be used to estimate the proportion of units that have such defects and the parameters of the assumed time-to-failure distribution of the defective subpopulation. The purpose of this article is to outline methods for analyzing life test data from life tests for “limited-failure” populations. Applications are described and a numerical example is included.

ISSN:0040-1706    

DOI:10.1080/00401706.1987.10488183

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

We present the results of a Monte Carlo study of the leading methods for constructing approximate confidence regions and confidence intervals for parameters estimated by nonlinear least squares. We examine three variants of the linearization method, the likelihood method, and the lack-of-fit method. The linearization method is computationally inexpensive, produces easily understandable results, and is widely used in practice. The likelihood and lack-of-fit methods are much more expensive and more difficult to report. In our tests, both the likelihood and lack-of-fit methods perform very reliably. All three variants of the linearization method, however, often grossly underestimate confidence regions and sometimes significantly underestimate confidence intervals. The linearization method variant based solely on the Jacobian matrix appears preferable to the two variants that use the full Hessian matrix because it is less expensive, more numerically stable, and at least as accurate. The Bates and Watts curvature measures are consistent with our results.

ISSN:0040-1706    

DOI:10.1080/00401706.1987.10488184

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

Symmetry of the error distribution is a common assumption in robust estimation of location and regression parameters. Tests for detecting asymmetry in the location problem are available, but their performance in regression situations is unknown. Here two such tests are investigated, and the evidence suggests two conclusions. First, the tests are valid when applied directly to either robust or least squares residuals as long as the number of parameters estimated is no more than a fourth of the sample size. Second, the effect of the design matrix on power for detecting a skewed error distribution is roughly characterized by a third-moment quantity based on least squares analysis.

ISSN:0040-1706    

DOI:10.1080/00401706.1987.10488185

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

Formulas are derived for the powers of two alternative lack-of-fit tests when regression data contain pure error. Approximations for these powers are compared for a specific example.

ISSN:0040-1706    

DOI:10.1080/00401706.1987.10488186

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

A novel test procedure is proposed to diagnose the goodness of fit of a simple regression model by applying a marginal likelihood under the assumption of smoothness of the alternative regression curve. No specific form for the alternative regression function is assumed. An advantage of the proposed test procedure is that it simultaneously provides an estimated regression curve (spline). Some existing diagnostic procedures are explored in relation to the one proposed. The procedure is applied to data of a spectrophotometric analysis of mixtures of two types of flour, cornstarch and casein (soybean).

ISSN:0040-1706    

DOI:10.1080/00401706.1987.10488187

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor