Hierarchical spatially varying coefficient and temporal dynamic process models using spTDyn

Bayesian hierarchical spatio-temporal models are becoming increasingly important due to the increasing availability of space-time data in various domains. In this paper we develop a user friendly R package, spTDyn, for spatio-temporal modelling. It can be used to fit models with spatially varying and temporally dynamic coefficients. The former is used for modelling the spatially varying impact of explanatory variables on the response caused by spatial misalignment. This issue can arise when the covariates only vary over time, or when they are measured over a grid and hence do not match the locations of the response point-level data. The latter is to examine the temporally varying impact of explanatory variables in space-time data due, for example, to seasonality or other time-varying effects. The spTDyn package uses Markov chain Monte Carlo sampling written in C, which makes computations highly efficient, and the interface is written in R making these sophisticated modelling techniques easily accessible to statistical analysts. The models and software, and their advantages, are illustrated using temperature and ozone space-time data.     

A fast algorithm for the coordinate-wise minimum distance estimation

Application of the minimum distance (MD) estimation method to the linear regression model for estimating regression parameters is a difficult and time-consuming process due to the complexity of its distance function, and hence, it is computationally expensive. To deal with the computational cost, this paper proposes a fast algorithm which makes the best use of coordinate-wise minimization technique in order to obtain the MD estimator. R package (KoulMde) based on the proposed algorithm and written in Rcpp is available online.     

Model selection in quantile regression models

Lasso methods are regularisation and shrinkage methods widely used for subset selection and estimation in regression problems. From a Bayesian perspective, the Lasso-type estimate can be viewed as a Bayesian posterior mode when specifying independent Laplace prior distributions for the coefficients of independent variables [32 T. Park, G. Casella, The Bayesian Lasso, J. Amer. Statist. Assoc. 103 (2008), pp. 681–686. doi: 10.1198/016214508000000337[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]. A scale mixture of normal priors can also provide an adaptive regularisation method and represents an alternative model to the Bayesian Lasso-type model. In this paper, we assign a normal prior with mean zero and unknown variance for each quantile coefficient of independent variable. Then, a simple Markov Chain Monte Carlo-based computation technique is developed for quantile regression (QReg) models, including continuous, binary and left-censored outcomes. Based on the proposed prior, we propose a criterion for model selection in QReg models. The proposed criterion can be applied to classical least-squares, classical QReg, classical Tobit QReg and many others. For example, the proposed criterion can be applied to rq(), lm() and crq() which is available in an R package called Brq. Through simulation studies and analysis of a prostate cancer data set, we assess the performance of the proposed methods. The simulation studies and the prostate cancer data set analysis confirm that our methods perform well, compared with other approaches.     

Approximate tolerance intervals for the discrete Poisson–Lindley distribution

The Poisson–Lindley distribution is a compound discrete distribution that can be used as an alternative to other discrete distributions, like the negative binomial. This paper develops approximate one-sided and equal-tailed two-sided tolerance intervals for the Poisson–Lindley distribution. Practical applications of the Poisson–Lindley distribution frequently involve large samples, thus we utilize large-sample Wald confidence intervals in the construction of our tolerance intervals. A coverage study is presented to demonstrate the efficacy of the proposed tolerance intervals. The tolerance intervals are also demonstrated using two real data sets. The R code developed for our discussion is briefly highlighted and included in the tolerance package.     

Bayesian analysis of generalized elliptical semi-parametric models

In this paper, we study the statistical inference based on the Bayesian approach for regression models with the assumption that independent additive errors follow normal, Student-t, slash, contaminated normal, Laplace or symmetric hyperbolic distribution, where both location and dispersion parameters of the response variable distribution include nonparametric additive components approximated by B-splines. This class of models provides a rich set of symmetric distributions for the model error. Some of these distributions have heavier or lighter tails than the normal as well as different levels of kurtosis. In order to draw samples of the posterior distribution of the interest parameters, we propose an efficient Markov Chain Monte Carlo (MCMC) algorithm, which combines Gibbs sampler and Metropolis–Hastings algorithms. The performance of the proposed MCMC algorithm is assessed through simulation experiments. We apply the proposed methodology to a real data set. The proposed methodology is implemented in the R package BayesGESM using the function gesm().     

Modeling bivariate survival data using shared inverse Gaussian frailty model

ABSTRACT

The shared frailty models are often used to model heterogeneity in survival analysis. The most common shared frailty model is a model in which hazard function is a product of a random factor (frailty) and the baseline hazard function which is common to all individuals. There are certain assumptions about the baseline distribution and the distribution of frailty. In this paper, we consider inverse Gaussian distribution as frailty distribution and three different baseline distributions, namely the generalized Rayleigh, the weighted exponential, and the extended Weibull distributions. With these three baseline distributions, we propose three different inverse Gaussian shared frailty models. We also compare these models with the models where the above-mentioned distributions are considered without frailty. We develop the Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in these models. We present a simulation study to compare the true values of the parameters with the estimated values. A search of the literature suggests that currently no work has been done for these three baseline distributions with a shared inverse Gaussian frailty so far. We also apply these three models by using a real-life bivariate survival data set of McGilchrist and Aisbett (1991 McGilchrist, C.A., Aisbett, C.W. (1991). Regression with frailty in survival analysis. Biometrics 47:461–466.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) related to the kidney infection data and a better model is suggested for the data using the Bayesian model selection criteria.     

An Introduction to Practical Sequential Inferences via Single-Arm Binary Response Studies Using the binseqtest R Package

We review sequential designs, including group sequential and two-stage designs, for testing or estimating a single binary parameter. We use this simple case to introduce ideas common to many sequential designs, which in this case can be explained without explicitly using stochastic processes. We focus on methods provided by our newly developed R package, binseqtest, which exactly bound the Type I error rate of tests and exactly maintain proper coverage of confidence intervals. Within this framework, we review some allowable practical adaptations of the sequential design. We explore issues such as the following: How should the design be modified if no assessment was made at one of the planned sequential stopping times? How should the parameter be estimated if the study needs to be stopped early? What reasons for stopping early are allowed? How should inferences be made when the study is stopped for crossing the boundary, but later information is collected about responses of subjects that had enrolled before the decision to stop but had not responded by that time? Answers to these questions are demonstrated using basic methods that are available in our binseqtest R package. Supplementary materials for this article are available online.     

Objective Bayesian Analysis for Linear Degradation Models

We propose an objective Bayesian approach to analyze degradation models. For the linear degradation models, two reference priors are derived, and based on this we show the posterior distributions are proper. Since the lifetime of the product is of interest in practice, a transformation is introduced to obtain the reference priors of the medium lifetime. In the posterior analysis, we explore two sampling procedures: Monte Carlo (MC) procedure and Monte Carlo Markov Chain (MCMC) procedure. A real data from Takeda and Suzuki (1983 Takeda , E. , Suzuki , N. ( 1983 ). An empirical model for device degradation due to hot-carrier injection . IEEE Electron Dev. Lett. 4 : 111 – 113 .[Crossref], [Web of Science ®] , [Google Scholar]) is analyzed, and we find the results obtained by both procedures are close to the given literature.     

Likelihood-free parallel tempering

Approximate Bayesian Computational (ABC) methods, or likelihood-free methods, have appeared in the past fifteen years as useful methods to perform Bayesian analysis when the likelihood is analytically or computationally intractable. Several ABC methods have been proposed: MCMC methods have been developed by Marjoram et al. (2003) and by Bortot et al. (2007) for instance, and sequential methods have been proposed among others by Sisson et al. (2007), Beaumont et al. (2009) and Del Moral et al. (2012). Recently, sequential ABC methods have appeared as an alternative to ABC-PMC methods (see for instance McKinley et al., 2009; Sisson et al., 2007). In this paper a new algorithm combining population-based MCMC methods with ABC requirements is proposed, using an analogy with the parallel tempering algorithm (Geyer 1991). Performance is compared with existing ABC algorithms on simulations and on a real example.     

Analysis of censored longitudinal data with skewness and a terminal event

In HIV/AIDS study, the measurements viral load are often highly skewed and left-censored because of a lower detection limit. Furthermore, a terminal event (e.g., death) stops the follow-up process. The time to terminal event may be dependent on the viral load measurements. In this article, we present a joint analysis framework to model the censored longitudinal data with skewness and a terminal event process. The estimation is carried out by adaptive Gaussian quadrature techniques in SAS procedure NLMIXED. The proposed model is evaluated by a simulation study and is applied to the motivating Multicenter AIDS Cohort Study (MACS).     

DSGE Models with Student-t Errors

This paper deals with Dynamic Stochastic General Equilibrium (DSGE) models under a multivariate student-t distribution for the structural shocks. Based on the solution algorithm of Klein (2000) and the gamma-normal representation of the t-distribution, the TaRB-MH algorithm of Chib and Ramamurthy (2010 Chib , S. , Ramamurthy , S. ( 2010 ). Tailored randomized block MCMC methods with application to DSGE models . Journal of Econometrics 108 : 19 – 38 .[Crossref], [Web of Science ®] , [Google Scholar]) is used to estimate the model. A technique for estimating the marginal likelihood of the DSGE student-t model is also provided. The methodologies are illustrated first with simulated data and then with the DSGE model of Ireland (2004 Ireland , P. N. ( 2004 ). Technology shocks in the new keynesian model . Review of Economics and Statistics 86 ( 4 ): 923 – 936 .[Crossref], [Web of Science ®] , [Google Scholar]) where the results support the t-error model in relation to the Gaussian model.     

Knot selection for least-squares and penalized splines

Two new stochastic search methods are proposed for optimizing the knot locations and/or smoothing parameters for least-squares or penalized splines. One of the methods is a golden-section-augmented blind search, while the other is a continuous genetic algorithm. Monte Carlo experiments indicate that the algorithms are very successful at producing knot locations and/or smoothing parameters that are near optimal in a squared error sense. Both algorithms are amenable to parallelization and have been implemented in OpenMP and MPI. An adjusted GCV criterion is also considered for selecting both the number and location of knots. The method performed well relative to MARS in a small empirical comparison.     

Modeling of Inverse Gaussian Frailty Model for Bivariate Survival Data

Shared frailty models are often used to model heterogeneity in survival analysis. The most common shared frailty model is a model in which hazard function is a product of random factor (frailty) and baseline hazard function which is common to all individuals. There are certain assumptions about the baseline distribution and distribution of frailty. In this article, we consider inverse Gaussian distribution as frailty distribution and three different baseline distributions namely, Weibull, generalized exponential, and exponential power distribution. With these three baseline distributions, we propose three different inverse Gaussian shared frailty models. To estimate the parameters involved in these models we adopt Markov Chain Monte Carlo (MCMC) approach. We present a simulation study to compare the true values of the parameters with the estimated values. Also, we apply these three models to a real life bivariate survival data set of McGilchrist and Aisbett (1991 McGilchrist , C. A. , Aisbett , C. W. ( 1991 ). Regression with frailty in survival analysis . Biometrics 47 : 461 – 466 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) related to kidney infection and a better model is suggested for the data.     

Bayesian Estimation of Parameters and Comparison of Shared Gamma Frailty Models

In this article, we introduce shared gamma frailty models with three different baseline distributions namely, Weibull, generalized exponential and exponential power distributions. We develop Bayesian estimation procedure using Markov Chain Monte Carlo(MCMC) technique to estimate the parameters involved in these models. We present a simulation study to compare the true values of the parameters with the estimated values. Also we apply these three models to a real life bivariate survival dataset of McGilchrist and Aisbett (1991 McGilchrist, C. A. and Aisbett, C. W. 1991. Regression with frailty in survival analysis. Biometrics, 47: 461–466. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) related to kidney infection data and a better model is suggested for the data.     

Automatic model selection for high-dimensional survival analysis

Many different models for the analysis of high-dimensional survival data have been developed over the past years. While some of the models and implementations come with an internal parameter tuning automatism, others require the user to accurately adjust defaults, which often feels like a guessing game. Exhaustively trying out all model and parameter combinations will quickly become tedious or infeasible in computationally intensive settings, even if parallelization is employed. Therefore, we propose to use modern algorithm configuration techniques, e.g. iterated F-racing, to efficiently move through the model hypothesis space and to simultaneously configure algorithm classes and their respective hyperparameters. In our application we study four lung cancer microarray data sets. For these we configure a predictor based on five survival analysis algorithms in combination with eight feature selection filters. We parallelize the optimization and all comparison experiments with the BatchJobs and BatchExperiments R packages.     

Generalized Tobit models: diagnostics and application in econometrics

The standard Tobit model is constructed under the assumption of a normal distribution and has been widely applied in econometrics. Atypical/extreme data have a harmful effect on the maximum likelihood estimates of the standard Tobit model parameters. Then, we need to count with diagnostic tools to evaluate the effect of extreme data. If they are detected, we must have available a Tobit model that is robust to this type of data. The family of elliptically contoured distributions has the Laplace, logistic, normal and Student-t cases as some of its members. This family has been largely used for providing generalizations of models based on the normal distribution, with excellent practical results. In particular, because the Student-t distribution has an additional parameter, we can adjust the kurtosis of the data, providing robust estimates against extreme data. We propose a methodology based on a generalization of the standard Tobit model with errors following elliptical distributions. Diagnostics in the Tobit model with elliptical errors are developed. We derive residuals and global/local influence methods considering several perturbation schemes. This is important because different diagnostic methods can detect different atypical data. We implement the proposed methodology in an R package. We illustrate the methodology with real-world econometrical data by using the R package, which shows its potential applications. The Tobit model based on the Student-t distribution with a small quantity of degrees of freedom displays an excellent performance reducing the influence of extreme cases in the maximum likelihood estimates in the application presented. It provides new empirical evidence on the capabilities of the Student-t distribution for accommodation of atypical data.     

One-Sided Estimating and Testing Problems for Scale Models from Grouped Samples

Abstract

This article mainly analyzes estimating and testing problems for scale models from grouped samples. Suppose the support region of a density function, which does not depend on parameters, is divided into some disjoint intervals, grouped samples are the number of observations falling in each intervals respectively. The studying of grouped samples may be dated back to the beginning of the century, in which only one sample location and/or scale models is considered. (Shi, N.-Z., Gao, W., Zhang, B.-X. (2001 Shi, N.-Z., Gao, W. and Zhang, B.-X. 2001. One-sided estimating and testing problems for location models from grouped samples. Comm. Statist.—Simul. Comput, 30(4): 895–898.  [Google Scholar]). One-sided estimating and testing problems for location models from grouped samples. Comm. Statist.—Simul. Comput. 30(4)) had investigated one-sided problems for location models, this article discusses one-sided estimating and testing problems for scale models. Some algorithms for obtaining the maximum likelihood estimates of the parameters subject to order restrictions are proposed.     

Adaptive LASSO for linear regression models with ARMA-GARCH errors

The linear regression models with the autoregressive moving average (ARMA) errors (REGARMA models) are often considered, in order to reflect a serial correlation among observations. In this article, we focus on an adaptive least absolute shrinkage and selection operator (LASSO) (ALASSO) method for the variable selection of the REGARMA models and extend it to the linear regression models with the ARMA-generalized autoregressive conditional heteroskedasticity (ARMA-GARCH) errors (REGARMA-GARCH models). This attempt is an extension of the existing ALASSO method for the linear regression models with the AR errors (REGAR models) proposed by Wang et al. in 2007 Wang, H., Li, G., Tsai, C. (2007). Regression coefficient and autoregressive order shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B 69:63–78. [Google Scholar]. New ALASSO algorithms are proposed to determine important predictors for the REGARMA and REGARMA-GARCH models. Finally, we provide the simulation results and real data analysis to illustrate our findings.     

Test for Trend With a Multinomial Outcome

ABSTRACT

There is no established procedure for testing for trend with nominal outcomes that would provide both a global hypothesis test and outcome-specific inference. We derive a simple formula for such a test using a weighted sum of Cochran–Armitage test statistics evaluating the trend in each outcome separately. The test is shown to be equivalent to the score test for multinomial logistic regression, however, the new formulation enables the derivation of a sample size formula and multiplicity-adjusted inference for individual outcomes. The proposed methods are implemented in the R package multiCA.     

Tukey-Type Distributions in the Context of Financial Data

Abstract

In one-parameter (θ) families, we were not aware of explicit hypothesis testing scenarios where maximal invariant statistics failed to distinguish the models. We start with a concrete example (Sec. 2.2) to highlight such a hypothesis testing problem involving markedly different models. In this problem, because of the absence of a nontrivial uniformly most powerful invariant (UMPI) test, we briefly suggest two approaches to test the hypothesis. The first resolution (Sec. 3.1) is frequentist in nature. It utilizes a weight function on the parameter space and compares “average” distributions obtained under the null and alternative models in the sense of Wald (1947 Wald , A. ( 1947 ). Sequential Analysis . New York : Wiley . [Google Scholar] 1950 Wald , A. ( 1950 ). Statistical Decision Functions . New York : Wiley . [Google Scholar]). In contrast, a fully Bayesian resolution (Sec. 3.2) is also included. The note ends with a series of other interesting examples involving one-parameter families where maximal invariant statistics fail to distinguish the hypothesized models. The examples include easy-to-construct families of probability models involving only a single location or scale parameter θ.