摘要:

General formulas are derived for the asymptotic bias in regression coefficients and variance components estimated by penalized quasi-likelihood (PQL) in generalized linear mixed models with canonical link function and multiple sets of independent random effects. Easily computed correction matrices result in variance component estimates that have satisfactory asymptotic behavior for small values of the variance components and significantly reduce bias for larger values. Both first-order and second-order correction procedures are developed for regression coefficients estimated by PQL. The methods are illustrated through an analysis of an experiment on salamander matings involving crossed male and female random effects, and their properties are evaluated in a simulation study.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476971

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Numerical and asymptotic stochastic partitioning of goodness-of-fit statistics are considered for a broad class of simultaneous multivariate categorical response models. These simultaneous models impose constraints on the joint and marginal distributions of categorical response variables. Under certain conditions, the tenability of the corresponding simultaneous hypothesis can be assessed by separately testing the two subhypotheses: one regarding the joint distributions and the other regarding the marginal distributions. Specifically, easily verifiable sufficient conditions are introduced that allow us to partition the overall goodness-of-fit statistic into two interesting goodness-of-fit statistics: one for testing whether the joint distribution model holds and the other for testing whether the marginal distribution model holds. Moreover, it is proven that when the sufficient conditions hold and the simultaneous hypothesis is true, the two component goodness-of-fit statistics are asymptotically independent. These results are illustrated through several examples.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476972

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

This article constructs statistical models for clustered ordinal measurements. We specify two regression models: one for the marginal means and one for the marginal pairwise global odds ratios. Of particular interest are problems in which the odds ratio regression is a focus. Simple assumptions about higher-order conditional moments give a quadratic exponential likelihood function with second-order estimating equations (GEE2) as score equations. But computational difficulty can arise for large clusters when both the mean response and the association between measures is of interest. First, we present GEE1 as an alternative estimation strategy. Second, we extend to repeated ordinal measurements the method developed by Carey et al. for binary observations that is based on alternating logistic regressions (ALR) for the marginal mean parameters and the pairwise log-odds ratio parameters. We study the efficiency of GEE1 and ALR relative to full maximum likelihood. We demonstrate the utility of our regression methods for ordinal data by applying the methods to a surgical follow-up study.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476973

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Generating functions provide a simple and elegant way to describe probability or frequency distributions of discrete statistics and, in particular, permutation distributions. They are also a computational tool. Many efficient algorithms, including those described as fast Fourier transform methods, network methods, and multiple shift methods, are different implementations of the recursions needed to evaluate generating functions efficiently. Our goals here are twofold. First, we make the relationship between these efficient methods and generating functions explicit; this establishes a language for looking at other questions in randomization/exact inference and may help in finding more efficient implementations. Second, we propose methods to examine the sensitivity of results of exact analysis of discrete data to small perturbations in the data. Specifically, we consider two settings: how the analysis would change if one outcome changed, and how the analysis would change if one observation was added to the data set. Many of the computations needed to do a single exact analysis can be reused to study sensitivity; looking at this problem as one of computing generating functions makes the relationship explicit.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476974

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

New insights are given into why the problem of detecting multivariate outliers can be difficult and why the difficulty increases with the dimension of the data. Significant improvements in methods for detecting outliers are described, and extensive simulation experiments demonstrate that a hybrid method extends the practical boundaries of outlier detection capabilities. Based on simulation results and examples from the literature, the question of what levels of contamination can be detected by this algorithm as a function of dimension, computation time, sample size, contamination fraction, and distance of the contamination from the main body of data is investigated. Software to implement the methods is available from the authors and STATLIB.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476975

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The importance of pivoting is well established in the context of nonparametric confidence regions. It ensures enhanced coverage accuracy. However, pivoting for directional data cannot be achieved simply by rescaling. A somewhat cumbersome pivotal method, which involves passing first into a space of higher dimension, has been developed by Fisher and Hall for samples of unit vectors. Although that method has some advantages over nonpivotal techniques, it does suffer from certain drawbacks—in particular, the operation of passing to a higher dimension. Here we suggest alternative pivotal approaches, the implementation of which does not require us to increase the intrinsic dimension of the data and which in practice seem to achieve greater coverage accuracy. These methods are of two types: new pivotal bootstrap techniques and techniques that exploit the “implicit pivotalness” of the empirical likelihood algorithm. Unlike the method proposed by Fisher and Hall, these methods are also applicable to axial data and lead to the first pivotal, small-sample nonparametric confidence methods for mean principal or polar axes.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476976

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Monte Carlo tests have exact level when the distribution of the test statistic is free of nuisance parameters. Confidence sets obtained by inverting such tests are also exact but may have a complicated structure. The sets reduce to intervals if the sampling can be organized in a special way. A sufficient condition is that the test statistic is monotone in the parameter of interest when all random drawings are kept fixed. Examples given include models from the one-parameter exponential class. A simple theory quantifying the impact of Monte Carlo uncertainty is also developed.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476977

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

A method is proposed for reconstructing images from tomographic data with respect to a two-dimensional wavelet basis. The Wavelet-vaguelette decomposition (WVD) is used as a framework within which expressions for the necessary wavelet coefficients may be derived. These coefficients are calculated using a version of the filtered back-projection algorithm as a computational tool, in a multiresolution fashion. The necessary filters are defined in terms of the underlying wavelets. Denoising is accomplished through an adaptation of the wavelet shrinkage (WS) approach of Donoho et al. and amounts to a form of regularization. Combining these two steps yields the proposed WVD/WS reconstruction algorithm, which is compared to the traditional filtered backprojection method in a small study.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476978

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The directional neighborhoods approach (DNA) to classifying pixels and reconstructing images from remotely sensed noisy data is a newly proposed computer-intensive procedure that is partly Bayesian and partly data analytic. It uses the observational data to select an optimal, generally asymmetric, but relatively homogeneous neighborhood for contextually classifying pixels. A criterion for “homogeneity of neighborhood” is developed. DNA involves two stages: a zero-neighbor preclassification stage, followed by selection of the most homogeneous neighborhood, and then a final classification. We provide Monte Carlo simulations for a two-population image and compare DNA results with those from a reference Bayesian contextual classification. We show that DNA improves substantially on the reference classification procedure.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476979

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

In the statistical analysis of survival data arising from two populations, it often happens that the analyst knows, a priori, that the life lengths in one population are stochastically shorter than those in the other. Nevertheless, survival probability estimates, if determined separately from the corresponding samples, may not be consistent with this prior assumption, because of inherent statistical variability in the observations. This problem has been considered in a number of papers during the past decade, by adopting a (generalized) maximum likelihood approach. Our approach is Bayesian and, in essence, nonparametric. The a priori assumption regarding stochastic ordering is formulated naturally in terms of a joint prior distribution defined for pairs of survival functions. Nonparametric specification of the model, based on hazard rates and using a few hyperparameters, allows for sufficient flexibility in practical applications. The numerical computations are based on a coupled version of the Metropolis—Hastings algorithm. The results from a statistical analysis are summarized nicely by a pair of predictive survival functions that are consistent with the assumed stochastic ordering.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476980

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor