Empirical Likelihood Semiparametric Regression Analysis under Random Censorship

This paper considers large sample inference for the regression parameter in a partly linear model for right censored data. We introduce an estimated empirical likelihood for the regression parameter and show that its limiting distribution is a mixture of central chi-squared distributions. A Monte Carlo method is proposed to approximate the limiting distribution. This enables one to make empirical likelihood-based inference for the regression parameter. We also develop an adjusted empirical likelihood method which only appeals to standard chi-square tables. Finite sample performance of the proposed methods is illustrated in a simulation study.     

Efficient Bayesian Inference for Multivariate Probit Models With Sparse Inverse Correlation Matrices

We propose a Bayesian approach for inference in the multivariate probit model, taking into account the association structure between binary observations. We model the association through the correlation matrix of the latent Gaussian variables. Conditional independence is imposed by setting some off-diagonal elements of the inverse correlation matrix to zero and this sparsity structure is modeled using a decomposable graphical model. We propose an efficient Markov chain Monte Carlo algorithm relying on a parameter expansion scheme to sample from the resulting posterior distribution. This algorithm updates the correlation matrix within a simple Gibbs sampling framework and allows us to infer the correlation structure from the data, generalizing methods used for inference in decomposable Gaussian graphical models to multivariate binary observations. We demonstrate the performance of this model and of the Markov chain Monte Carlo algorithm on simulated and real datasets. This article has online supplementary materials.     

Semiparametric quantile regression with random censoring

This paper considers estimation and inference in semiparametric quantile regression models when the response variable is subject to random censoring. The paper considers both the cases of independent and dependent censoring and proposes three iterative estimators based on inverse probability weighting, where the weights are estimated from the censoring distribution using the Kaplan–Meier, a fully parametric and the conditional Kaplan–Meier estimators. The paper proposes a computationally simple resampling technique that can be used to approximate the finite sample distribution of the parametric estimator. The paper also considers inference for both the parametric and nonparametric components of the quantile regression model. Monte Carlo simulations show that the proposed estimators and test statistics have good finite sample properties. Finally, the paper contains a real data application, which illustrates the usefulness of the proposed methods.

     

Variational Markov chain Monte Carlo for Bayesian smoothing of non-linear diffusions

In this paper we develop set of novel Markov chain Monte Carlo algorithms for Bayesian smoothing of partially observed non-linear diffusion processes. The sampling algorithms developed herein use a deterministic approximation to the posterior distribution over paths as the proposal distribution for a mixture of an independence and a random walk sampler. The approximating distribution is sampled by simulating an optimized time-dependent linear diffusion process derived from the recently developed variational Gaussian process approximation method. The novel diffusion bridge proposal derived from the variational approximation allows the use of a flexible blocking strategy that further improves mixing, and thus the efficiency, of the sampling algorithms. The algorithms are tested on two diffusion processes: one with double-well potential drift and another with SINE drift. The new algorithm’s accuracy and efficiency is compared with state-of-the-art hybrid Monte Carlo based path sampling. It is shown that in practical, finite sample applications the algorithm is accurate except in the presence of large observation errors and low observation densities, which lead to a multi-modal structure in the posterior distribution over paths. More importantly, the variational approximation assisted sampling algorithm outperforms hybrid Monte Carlo in terms of computational efficiency, except when the diffusion process is densely observed with small errors in which case both algorithms are equally efficient.     

Correcting for Simulation Bias in Monte Carlo Methods to Value Exotic Options in Models Driven by Lévy Processes

Lévy processes can be used to model asset return's distributions. Monte Carlo methods must frequently be used to value path dependent options in these models, but Monte Carlo methods can be prone to considerable simulation bias when valuing options with continuous reset conditions. This paper shows how to correct for this bias for a range of options by generating a sample from the extremes distribution of the Lévy process on subintervals. The method uses variance‐gamma and normal inverse Gaussian processes. The method gives considerable reductions in bias, so that it becomes feasible to apply variance reduction methods. The method seems to be a very fruitful approach in a framework in which many options do not have analytical solutions.     

Bayesian and Maximum Likelihood Estimation for Gaussian Processes on an Incomplete Lattice

This article proposes a new approach for Bayesian and maximum likelihood parameter estimation for stationary Gaussian processes observed on a large lattice with missing values. We propose a Markov chain Monte Carlo approach for Bayesian inference, and a Monte Carlo expectation-maximization algorithm for maximum likelihood inference. Our approach uses data augmentation and circulant embedding of the covariance matrix, and provides likelihood-based inference for the parameters and the missing data. Using simulated data and an application to satellite sea surface temperatures in the Pacific Ocean, we show that our method provides accurate inference on lattices of sizes up to 512 × 512, and is competitive with two popular methods: composite likelihood and spectral approximations.     

Goodness-of-fit tests based on the empirical characteristic function

The paper is devoted to the supremum-type multivariate goodness-of-fit tests based on the empirical characteristic function. Particular attention is devoted to the composite hypothesis of normality and Gaussian distribution mixture model. An analytical way to approximate the null asymptotic distributions of the considered test statistics is discussed applying the theory of large excursions of differentiable Gaussian random fields. The produced comparative Monte Carlo power study shows that the considered tests are powerful competitors to the existing classical criteria, clearly dominating in verification of the goodness-of-fit hypotheses against the specific types of alternatives.     

Estimation of coefficient of variation in a weighted inverse Gaussian model

The coefficient of variation is an important parameter in many physical, biological and medical sciences. In this paper we study the estimation of the square of the coefficient of variation in a weighted inverse Gaussian model which is a mixture of the inverse Gaussian and the length biased inverse Gaussian distribution. This represents a rich family of distributions for different values of the mixing parameter and can be used for modelling various life testing situations. The maximum likelihood as well as the Bayes estimates of the parameters are obtained. These estimates are used to derive the estimates of the square of the coefficient of variation of the model under study. Several important data sets are analysed to illustrate the results. © 1996 John Wiley & Sons, Ltd.     

A Marginal Sampler for σ-Stable Poisson–Kingman Mixture Models

We investigate the class of σ-stable Poisson–Kingman random probability measures (RPMs) in the context of Bayesian nonparametric mixture modeling. This is a large class of discrete RPMs, which encompasses most of the popular discrete RPMs used in Bayesian nonparametrics, such as the Dirichlet process, Pitman–Yor process, the normalized inverse Gaussian process, and the normalized generalized Gamma process. We show how certain sampling properties and marginal characterizations of σ-stable Poisson–Kingman RPMs can be usefully exploited for devising a Markov chain Monte Carlo (MCMC) algorithm for performing posterior inference with a Bayesian nonparametric mixture model. Specifically, we introduce a novel and efficient MCMC sampling scheme in an augmented space that has a small number of auxiliary variables per iteration. We apply our sampling scheme to a density estimation and clustering tasks with unidimensional and multidimensional datasets, and compare it against competing MCMC sampling schemes. Supplementary materials for this article are available online.     

指数分布2/3(G)表决系统产品的统计分析

针对指数分布2/3(G)表决系统产品,本文给出了系统的寿命分布及数字特征,并在全样本场合下给出了参数的矩估计、极大似然估计和逆矩估计,通过大量Monte-Carlo模拟比较了三种点估计的精度。此外,还给出了求参数区间估计的两种方法,并通过大量Monte-Carlo模拟考察了区间估计的精度,得到参数的精确区间估计优于近似区间估计。     

Implementing random scan Gibbs samplers

Summary  The Gibbs sampler, being a popular routine amongst Markov chain Monte Carlo sampling methodologies, has revolutionized the application of Monte Carlo methods in statistical computing practice. The performance of the Gibbs sampler relies heavily on the choice of sweep strategy, that is, the means by which the components or blocks of the random vector X of interest are visited and updated. We develop an automated, adaptive algorithm for implementing the optimal sweep strategy as the Gibbs sampler traverses the sample space. The decision rules through which this strategy is chosen are based on convergence properties of the induced chain and precision of statistical inferences drawn from the generated Monte Carlo samples. As part of the development, we analytically derive closed form expressions for the decision criteria of interest and present computationally feasible implementations of the adaptive random scan Gibbs sampler via a Gaussian approximation to the target distribution. We illustrate the results and algorithms presented by using the adaptive random scan Gibbs sampler developed to sample multivariate Gaussian target distributions, and screening test and image data. Research by RL and ZY supported in part by a US National Science Foundation FRG grant 0139948 and a grant from Lawrence Livermore National Laboratory, Livermore, California, USA.     

Inducing normality from non‐Gaussian long memory time series and its application to stock return data

Motivated by Lee and Ko (Appl. Stochastic Models. Bus. Ind. 2007; 23 :493–502) but not limited to the study, this paper proposes a wavelet‐based Bayesian power transformation procedure through the well‐known Box–Cox transformation to induce normality from non‐Gaussian long memory processes. We consider power transformations of non‐Gaussian long memory time series under the assumption of an unknown transformation parameter, a situation that arises commonly in practice, while most research has been devoted to non‐linear transformations of Gaussian long memory time series with known transformation parameter. Specially, this study is mainly focused on the simultaneous estimation of the transformation parameter and long memory parameter. To this end, posterior estimations via Markov chain Monte Carlo methods are performed in the wavelet domain. Performances are assessed on a simulation study and a German stock return data set. Copyright © 2009 John Wiley & Sons, Ltd.     

Score tests for zero-inflated double poisson regression models

Count data with excess zeros encountered in many applications often exhibit extra variation. Therefore, zero-inflated Poisson (ZIP) model may fail to fit such data. In this paper, a zero-inflated double Poisson model (ZIDP), which is generalization of the ZIP model, is studied and the score tests for the significance of dispersion and zero-inflation in ZIDP model are developed. Meanwhile, this work also develops homogeneous tests for dispersion and/or zero-inflation parameter, and corresponding score test statistics are obtained. One numerical example is given to illustrate our methodology and the properties of score test statistics are investigated through Monte Carlo simulations.     

Heteroscedasticity and/or Autocorrelation Checks in Longitudinal Nonlinear Models with Elliptical and AR（1） Errors

The aim of this paper is to study the tests for variance heterogeneity and/or autocorrelation in nonlinear regression models with elliptical and AR(1) errors. The elliptical class includes several symmetric multivariate distributions such as normal, Student-t, power exponential, among others. Several diagnostic tests using score statistics and their adjustment are constructed. The asymptotic properties, including asymptotic chi-square and approximate powers under local alternatives of the score statistics, are studied. The properties of test statistics are investigated through Monte Carlo simulations. A data set previously analyzed under normal errors is reanalyzed under elliptical models to illustrate our test methods.     

Varying coefficients partially linear models with randomly censored data

This paper considers the problem of estimation and inference in semiparametric varying coefficients partially linear models when the response variable is subject to random censoring. The paper proposes an estimator based on combining inverse probability of censoring weighting and profile least squares estimation. The resulting estimator is shown to be asymptotically normal. The paper also proposes a number of test statistics that can be used to test linear restrictions on both the parametric and nonparametric components. Finally, the paper considers the important issue of correct specification and proposes a nonsmoothing test based on a Cramer von Mises type of statistic, which does not suffer from the curse of dimensionality, nor requires multidimensional integration. Monte Carlo simulations illustrate the finite sample properties of the estimator and test statistics.     

Efficient statistical inference for partially nonlinear errors-in-variables models

In this paper, we consider the partially nonlinear errors-in-variables models when the non- parametric component is measured with additive error. The profile nonlinear least squares estimator of unknown parameter and the estimator of nonparametric component are constructed, and their asymptotic properties are derived under general assumptions. Finite sample performances of the proposed statistical inference procedures are illustrated by Monte Carlo simulation studies.     

Penalized Empirical Likelihood Estimation for Partially Linear Single Index Panel Model with Fixed Effects

This paper constructs a penalized empirical likelihood estimation method via quadratic inference function method, filter method and empirical likelihood estimation method. Under some regular conditions, we derived the large sample properties of estimators and show that the proposed empirical likelihood ratio is asymptotically to chi-square distribution. Furthermore, the infinite sample performance of the proposed method is evaluated by Monte Carlo simulation and real data analysis.     

Testing for equality between two copulas

We develop a test of equality between two dependence structures estimated through empirical copulas. We provide inference for independent or paired samples. The multiplier central limit theorem is used for calculating p-values of the Cramér-von Mises test statistic. Finite sample properties are assessed with Monte Carlo experiments. We apply the testing procedure on empirical examples in finance, psychology, insurance and medicine.     

A new instrumental variable estimation for diffusion processes

We consider the problem of parametric inference from continuous sample paths of the diffusion processes {x(t)} generated by the system of possibly nonstationary and/or nonlinear Ito stochastic differential equations. We propose a new instrumental variable estimator of the parameter whose pivotal statistic has a Gaussian distribution for all possible values of parameter. The new estimator enables us to construct exact level-α confidence intervals and tests for the parameter in the possibly non-stationary and/or nonlinear diffusion processes. Applications to several non-stationary and/or nonlinear diffusion processes are considered as examples. This work was supported by Korea Research Foundation Grant (KRF-2001-015-DP0057).     

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??This paper constructs a penalized empirical likelihood estimation method via quadratic inference function method, filter method and empirical likelihood estimation method. Under some regular conditions, we derived the large sample properties of estimators and show that the proposed empirical likelihood ratio is asymptotically to chi-square distribution. Furthermore, the infinite sample performance of the proposed method is evaluated by Monte Carlo simulation and real data analysis.