Parallel tempering for dynamic generalized linear models

ABSTRACT

Markov chain Monte Carlo (MCMC) methods can be used for statistical inference. The methods are time-consuming due to time-vary. To resolve these problems, parallel tempering (PT), as a parallel MCMC method, is tried, for dynamic generalized linear models (DGLMs), as well as the several optimal properties of our proposed method. In PT, two or more samples are drawn at the same time, and samples can exchange information with each other. We also present some simulations of the DGLMs in the case and provide two applications of Poisson-type DGLMs in financial research.     

Empirical Likelihood for Single-Index Regression Models under Negatively Associated Errors

In this article, we use bockwise empirical likelihood technique to construct confidence regions for the parameter of the single-index models under negatively associated errors. It is shown that the blockwise empirical likelihood ratio statistic for the parameter of interest is asymptotically χ²-type distributed. The result can be used to obtain confidence regions for the parameter of interest.     

Additive Transformation Models for Recurrent Events

In this article, we propose a class of additive transformation models for recurrent event data, which includes the additive rates model as a special case. The new models offer great flexibility in formulating the effects of covariates on the mean function of recurrent events. Estimating equation approaches are developed for the model parameters, and asymptotic properties of the resulting estimators are established. In addition, a model checking procedure is presented to assess the adequacy of the model. The finite sample performance of the proposed estimators is examined through simulation studies, and an application to a bladder cancer study is presented.     

Empirical Likelihood Inference for the Parameter in Additive Partially Linear EV Models

In this article, we consider empirical likelihood inference for the parameter in the additive partially linear models when the linear covariate is measured with error. By correcting for attenuation, a corrected-attenuation empirical log-likelihood ratio statistic for the unknown parameter β, which is of primary interest, is suggested. We show that the proposed statistic is asymptotically standard chi-square distribution without requiring the undersmoothing of the nonparametric components, and hence it can be directly used to construct the confidence region for the parameter β. Some simulations indicate that, in terms of comparison between coverage probabilities and average lengths of the confidence intervals, the proposed method performs better than the profile-based least-squares method. We also give the maximum empirical likelihood estimator (MELE) for the unknown parameter β, and prove the MELE is asymptotically normal under some mild conditions.     

Estimation Bias in Complete-Case Analysis in Crossover Studies with Missing Data

Crossover designs are used often in clinical trials. It is not uncommon that subjects discontinue before completing all treatment periods in a crossover study. Despite availability of statistical methodologies utilizing all available data and software for obtaining valid inferences under the assumption of missing at random (MAR), naïve approaches, such as the complete case (CC) analysis, which is only valid with a strong assumption of missing completely at random are still widely used in practice. In this article, we obtain the analytical form of the estimation bias of treatment effects with CC for linear mixed models. We use simulation studies to examine the inflation of Type I error and efficiency loss in the inferences with CC under MAR. Invalidity and inefficiency of two other commonly used approaches for defining analyzed data in the presence of missing data, including data from at least two periods in three period crossover and available cases for a specific comparison of interest, are also demonstrated through simulation studies.     

Statistical Properties of a Modified Accelerated Design for Phase I Cancer Clinical Trials

We consider the semiparametric profile likelihood inference for the distribution function under doubly censored data. For further developments of the statistical inference based on the profile likelihood ratio and alternative tools such as the score or Wald-type inference, we discuss the structures of the profile likelihood estimators and their derivatives included in the score function and the Fisher function of the profile likelihood, establishing the consistencies of their estimators.     

Robust Confidence Intervals for the Bernoulli Parameter

Despite the simplicity of the Bernoulli process, developing good confidence interval procedures for its parameter—the probability of success p—is deceptively difficult. The binary data yield a discrete number of successes from a discrete number of trials, n. This discreteness results in actual coverage probabilities that oscillate with the n for fixed values of p (and with p for fixed n). Moreover, this oscillation necessitates a large sample size to guarantee a good coverage probability when p is close to 0 or 1.

It is well known that the Wilson procedure is superior to many existing procedures because it is less sensitive to p than any other procedures, therefore it is less costly. The procedures proposed in this article work as well as the Wilson procedure when 0.1 ≤p ≤ 0.9, and are even less sensitive (i.e., more robust) than the Wilson procedure when p is close to 0 or 1. Specifically, when the nominal coverage probability is 0.95, the Wilson procedure requires a sample size 1, 021 to guarantee that the coverage probabilities stay above 0.92 for any 0.001 ≤ min {p, 1 ?p} <0.01. By contrast, our procedures guarantee the same coverage probabilities but only need a sample size 177 without increasing either the expected interval width or the standard deviation of the interval width.     

Multiplicative Adjustment Method for Semiparametric Regression with Mixing Dependent Data

In this article, we extend a semiparametric regression estimator with multiplicative adjustment to time series context. The asymptotic theory and results from a simulation study are discussed. Theoretical results and numerical comparison show that, in the time series case, the semiparametric estimator is better than the traditional local polynomial estimator in a wide neighbourhood around the true regression function.