摘要:

The logit, probit, and studentt-links are widely used in modeling dichotomous quantal response data. Most of the commonly used link functions are symmetric, except the complementary log-log link. However, in some applications the overall fit can be significantly improved by the use of an asymmetric link. In this article we propose a new skewed link model for analyzing binary response data with covariates. Introducing a skewed distribution for the underlying latent variable, we develop a class of asymmetric link models for binary response data. Using a Bayesian approach, we first characterize the propriety of the posterior distributions using standard improper priors. We further propose informative priors using historical data from a similar previous study. We examine the proposed method through a large-scale simulation study and use data from a prostate cancer study to demonstrate the use of historical data in Bayesian model fitting and comparison of skewed link models.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10473872

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

The idea of dimension reduction without loss of information can be quite helpful for guiding the construction of summary plots in regression without requiring a prespecified model. Focusing on the central subspace, we investigate such “sufficient” dimension reduction in regressions with a binary response. Three existing methods—sliced inverse regression, principal Hessian direction, and sliced average variance estimation—and one new method—difference of covariances—are studied for their ability to estimate the central subspace and produce sufficient summary plots. Combining these numerical methods with the graphical methods proposed earlier by Cook leads to a novel paradigm for the analysis of binary response regressions.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10473873

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

The standardized spectral density completely describes serial dependence of a Gaussian process. For non-Gaussian processes, however, it may become an inappropriate analytic tool, because it misses the nonlinear processes with zero autocorrelation. By generalizing the concept of the standardized spectral density, I propose a new spectral tool suitable for both linear and nonlinear time series analysis. The generalized spectral density is indexed by frequency and a pair of auxiliary parameters. It is well defined for both continuous and discrete random variables, and requires no moment condition. Introduction of the auxiliary parameters renders the spectrum able to capture all pairwise dependencies, including those with zero autocorrelation. The standardized spectral density can be derived by properly differentiating the generalized spectral density with respect to the auxiliary parameters at the origin. The consistency of a class of Parzen's kernel-type estimators for the generalized spectral density is established, and their optimal convergence rates are derived using the integrated mean squared error criterion. A data-dependent asymptotically optimal bandwidth (or lag order) is introduced. The kernel estimators and their derivatives are applied to construct a class of asymptotically one-sided N(0, 1) tests for generic serial dependence and hypotheses on various specific aspects of serial dependence. The latter include serial uncorrelatedness, martingale, conditional homoscedasticity, conditional symmetry, and conditional homokurtosis. All of the proposed tests, which include Hong's spectral density test for serial correlation, can be derived from a unified framework. An empirical application to Deutschemark exchange rates highlights the approach.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10473874

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

Recurrence time data can be regarded as a specific type of correlated survival data in which recurrent event times of a subject are stochastically ordered. Given the ordinal nature of recurrence times, this article focuses on conditional regression analysis. A semiparametric hazards model, including the structural and episode-specific parameters, is proposed for recurrence time data. In this model the order of episodes serves as the stratification variable. Estimation of the structural parameter can be constructed on the basis of all of the observed recurrence times. The structural parameter is estimated by the profile-likelihood approach. Although the structural parameter estimator is asymptotically normal, the episode-specific parameters may or may not be estimated consistently due to the sparseness of data for specific events. Examples are presented to illustrate the performance of the estimators of the structural and episode-specific parameters. An extension of the univariate recurrent events to the bivariate events, which occur repeatedly and sequentially, is discussed with an example.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10473875

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

We propose a new method of boundary correction for kernel density estimation. The technique is a kind of generalized reflection method involving reflecting a transformation of the data. The transformation depends on a pilot estimate of the logarithmic derivative of the density at the boundary. In simulations, the new method is seen to clearly outperform an earlier generalized reflection idea. It also has overall advantages over boundary kernel methods and a nonnegative adaptation thereof, although the latter are competitive in some situations. We also present the theory underlying the new methodology.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10473876

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

In this article we consider tests of variance components using Bayes factors. Such tests arise in many fields of application, including medicine, agriculture, and engineering. When using Bayes factors, the choice of prior distribution on the parameter of interest is of great importance; we propose a “unit-information” reference method for variance component models. The calculation of Bayes factors in this context is not straightforward; there are well-documented difficulties with Markov chain Monte Carlo approaches such as Gibbs sampling, and the usual Laplace approximation is not appropriate, due to the boundary null hypothesis. We describe both an importance sampling approach and an analytical approximation for calculating the numerator and denominator of the Bayes factor. The importance sampling approach is straightforward to implement and also forms the basis for a rejection algorithm that allows generation of samples from the posterior distributions under the null and alternative hypotheses. We suggest that the proposal for the rejection algorithm be based on the likelihood of a subset of the data. For large samples, we develop a boundary Laplace approximation that is accurate to orderop1). We investigate the accuracy of the approximation via simulation, and examine its relationship to the Schwarz criterion. We illustrate the importance sampling/rejection method and boundary Laplace approximation on a number of examples, including a challenging two-way, highly unbalanced dataset and compare our methods with frequentist alternatives.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10473877

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

The problem of estimating a covariance matrix in small samples has been considered by several authors following early work by Stein. This problem can be especially important in hierarchical models where the standard errors of fixed and random effects depend on estimation of the covariance matrix of the distribution of the random effects. We propose a set of hierarchical priors (HPs) for the covariance matrix that produce posterior shrinkage toward a specified structure—here we examine shrinkage toward diagonality. We then address the computational difficulties raised by incorporating these priors, and nonconjugate priors in general, into hierarchical models. We apply a combination of approximation, Gibbs sampling (possibly with a Metropolis step), and importance reweighting to fit the models, and compare this hybrid approach to alternative Markov Chain Monte Carlo methods. Our investigation involves three alternative HPs. The first works with the spectral decomposition of the covariance matrix and produces both shrinkage of the eigenvalues toward each other and shrinkage of the rotation matrix toward the identity. The second produces shrinkage of the correlations toward 0, and the third uses a conjugate Wishart distribution to shrink toward diagonality. A simulation study shows that the first two HPs can be very effective in reducing small-sample risk, whereas the conjugate Wishart version sometimes performs very poorly. We evaluate the computational algorithm in the context of a normal nonlinear random-effects model and illustrate the methodology with a logistic random-effects model.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10473878

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

Viewing the observed data of a statistical model as incomplete and augmenting its missing parts are useful for clarifying concepts and central to the invention of two well-known statistical algorithms: expectation-maximization (EM) and data augmentation. Recently, Liu, Rubin, and Wu demonstrated that expanding the parameter space along with augmenting the missing data is useful for accelerating iterative computation in an EM algorithm. The main purpose of this article is to rigorously define a parameter expanded data augmentation (PX-DA) algorithm and to study its theoretical properties. The PX-DA is a special way of using auxiliary variables to accelerate Gibbs sampling algorithms and is closely related to reparameterization techniques. We obtain theoretical results concerning the convergence rate of the PX-DA algorithm and the choice of prior for the expansion parameter. To understand the role of the expansion parameter, we establish a new theory for iterative conditional sampling under the transformation group formulation, which generalizes the standard Gibbs sampler. Using the new theory, we show that the PX-DA algorithm with a Haar measure prior (often improper) for the expansion parameter is always proper and is optimal among a class of such algorithms including reparameterization.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10473879

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

In this article we investigate a class of single-index coefficient regression models under dependence. This includes many existing models, such as the smooth transition threshold autoregressive (STAR) model of Chan and Tong, the functional-coefficient autoregressive (FAR) model of Chen and Tsay, and the single-index model of Ichimura. Compared to the varying-coefficient model of Hastie and Tibshirani, our model can avoid the curse of dimensionality in multivariate nonparametric estimations. Another advantage of this model is that a threshold variable is chosen automatically. An estimation method is proposed, and the corresponding estimators are shown to be consistent and asymptotically normal. Some simulations and applications are also reported.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10473880

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

We develop simple approximations for the p values to use with regression models having linear or nonlinear parameter structure and normal or nonnormal error distribution; computer iteration then gives confidence intervals. Both frequentist and Bayesian versions are given. The approximations are derived from recent developments in likelihood analysis and have third-order accuracy. Also, for very small and medium-sized samples, the accuracy can typically be high. The likelihood basis of the procedure seems to provide the grounds for this general accuracy. Examples are discussed, and simulations record the distributional accuracy.

ISSN:0162-1459    

DOI:10.1080/01621459.1999.10473881

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor