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.     

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.     

Comparison of Bayesian models for production efficiency

In this paper, we use Markov Chain Monte Carlo (MCMC) methods in order to estimate and compare stochastic production frontier models from a Bayesian perspective. We consider a number of competing models in terms of different production functions and the distribution of the asymmetric error term. All MCMC simulations are done using the package JAGS (Just Another Gibbs Sampler), a clone of the classic BUGS package which works closely with the R package where all the statistical computations and graphics are done.     

Simultaneous inference of a misclassified outcome and competing risks failure time data

Ipsilateral breast tumor relapse (IBTR) often occurs in breast cancer patients after their breast conservation therapy. The IBTR status' classification (true local recurrence versus new ipsilateral primary tumor) is subject to error and there is no widely accepted gold standard. Time to IBTR is likely informative for IBTR classification because new primary tumor tends to have a longer mean time to IBTR and is associated with improved survival as compared with the true local recurrence tumor. Moreover, some patients may die from breast cancer or other causes in a competing risk scenario during the follow-up period. Because the time to death can be correlated to the unobserved true IBTR status and time to IBTR (if relapse occurs), this terminal mechanism is non-ignorable. In this paper, we propose a unified framework that addresses these issues simultaneously by modeling the misclassified binary outcome without a gold standard and the correlated time to IBTR, subject to dependent competing terminal events. We evaluate the proposed framework by a simulation study and apply it to a real data set consisting of 4477 breast cancer patients. The adaptive Gaussian quadrature tools in SAS procedure NLMIXED can be conveniently used to fit the proposed model. We expect to see broad applications of our model in other studies with a similar data structure.     

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.     

A Poisson geometric process approach for predicting drop-out and committed first-time blood donors

A Poisson geometric process (PGP) model is proposed to study individual blood donation patterns for a blood donor retention program. Extended from the geometric process (GP) model of Lam [16 Y. Lam, Geometric process and replacement problem, Acta Math. Appl. Sin. 4 (1988), pp. 366–377. doi: 10.1007/BF02007241[Crossref] , [Google Scholar]], the PGP model captures the rather pronounced trend patterns across clusters of donors via the ratio parameters in a mixture setting. Within the state-space modeling framework, it allows for overdispersion by equating the mean of the Poisson data distribution to a latent GP. Alternatively, by simply setting, the mean of the Poisson distribution to be the mean of a GP, it has equidispersion. With the group-specific mean and ratio functions, the mixture PGP model facilitates classification of donors into committed, drop-out and one-time groups. Based on only two years of observations, the PGP model nicely predicts donors’ future donations to foster timely recruitment decision. The model is implemented using a Bayesian approach via the user-friendly software WinBUGS.     

Bayesian analysis of Cannabis offences using generalized Poisson geometric process model with flexible dispersion

ABSTRACT

This paper derives models to analyse Cannabis offences count series from New South Wales, Australia. The data display substantial overdispersion as well as underdispersion for a subset, trend movement and population heterogeneity. To describe the trend dynamic in the data, the Poisson geometric process model is first adopted and is extended to the generalized Poisson geometric process model to capture both over- and underdispersion. By further incorporating mixture effect, the model accommodates population heterogeneity and enables classification of homogeneous units. The model is implemented using Markov chain Monte Carlo algorithms via the user-friendly WinBUGS software and its performance is evaluated through a simulation study.     

Semicompeting risks in aging research: methods,issues and needs

A semicompeting risks problem involves two-types of events: a nonterminal and a terminal event (death). Typically, the nonterminal event is the focus of the study, but the terminal event can preclude the occurrence of the nonterminal event. Semicompeting risks are ubiquitous in studies of aging. Examples of semicompeting risk dyads include: dementia and death, frailty syndrome and death, disability and death, and nursing home placement and death. Semicompeting risk models can be divided into two broad classes: models based only on observables quantities (class \(\mathcal {O}\) ) and those based on potential (latent) failure times (class \(\mathcal {L}\) ). The classical illness-death model belongs to class \(\mathcal {O}\) . This model is a special case of the multistate models, which has been an active area of methodology development. During the past decade and a half, there has also been a flurry of methodological activity on semicompeting risks based on latent failure times ( \(\mathcal {L}\) models). These advances notwithstanding, the semicompeting risks methodology has not penetrated biomedical research, in general, and gerontological research, in particular. Some possible reasons for this lack of uptake are: the methods are relatively new and sophisticated, conceptual problems associated with potential failure time models are difficult to overcome, paucity of expository articles aimed at educating practitioners, and non-availability of readily usable software. The main goals of this review article are: (i) to describe the major types of semicompeting risks problems arising in aging research, (ii) to provide a brief survey of the semicompeting risks methods, (iii) to suggest appropriate methods for addressing the problems in aging research, (iv) to highlight areas where more work is needed, and (v) to suggest ways to facilitate the uptake of the semicompeting risks methodology by the broader biomedical research community.     

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.     

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.     

Evaluation of open items using the many-facet Rasch model

The goal of this study is to analyze the quality of ratings assigned to two constructed response questions for evaluating the written ability of essays in Portuguese language from the perspective of the many-facet Rasch (MFR [15 J.M. Linacre, Many-facet Rasch Measurement, 2nd ed., MESA Press, Chicago, 1994. [Google Scholar]]) model. The analyzed data set comes from 350 written tests with two open-item tasks that were developed based on a rating process independently marked by two rater coordinators and a group of 42 raters. The MFR model analysis shows the measurement quality related to the examinees, raters, tasks and items, and classification scale that has been used for the task rating process. The findings indicate significant differences amongst the rater severities and show that the raters cannot be interchanged. The results also suggest that the comparison between the two task difficulties needs further investigation. An additional study has been done on the scale structure of the classification used by each rater for each item. The result suggests that there have been some similarities amongst the tasks and a need of revision for some criteria of the rating process. Overall, the scale of evaluation has shown to be efficient for a classification of the examinees.     

A Marginalized Combined Gamma Frailty and Normal Random-effects Model for Repeated,Overdispersed, Time-to-event Outcomes

This article proposes a marginalized model for repeated or otherwise hierarchical, overdispersed time-to-event outcomes, adapting the so-called combined model for time-to-event outcomes of Molenberghs et al. (in press Molenberghs, G., Verbeke, G., Efendi, A., Braekers, R., Demétrio, C. G.B. (in press). A combined gamma frailty and normal random-effects model for repeated, overdispersed time-to-event data. In press. [Google Scholar]), who combined gamma and normal random effects. The two sets of random effects are used to accommodate simultaneously correlation between repeated measures and overdispersion. The proposed version allows for a direct marginal interpretation of all model parameters. The outcomes are allowed to be censored. Two estimation methods are proposed: full likelihood and pairwise likelihood. The proposed model is applied to data from a so-called comet assay and to data from recurrent asthma attacks in children. Both estimation methods perform very well. From simulation results, it follows that the marginalized combined model behaves similarly to the ordinary combined model in terms of point estimation and precision. It is also observed that the pairwise likelihood required more computation time on the one hand but is less sensitive to starting values and stabler in terms of bias with increasing sample size and censoring percentage than full likelihood, on the other, leaving room for both in practice.     

ON THE CONDITIONAL HOMOSCEDASTICITY TEST IN AUTOREGRESSIVE MODEL WITH ARCH ERROR

ABSTRACT

In this paper, we study the functional limiting law of the cumulative residual process associated to autoregression models with ARCH error when the data are assumed to be stationary and ergodic. Under homoscedasticity hypothesis of the model, it is stated that the limiting process is a time changed Wiener process plus a Gaussian random variable. On the basis of the law of the limiting process, we propose a chi-square type test to test the homoscedasticity hypothesis. A numerical comparisons of performances of our test, the Kolmogorov-Smirnov type test proposed by Chen and An[1] Chen, M. and An, H.Z. 1997. A Kolmogorov-Smirnov Type Test for Conditional Heteroscedaticity in Time Series. Statist. and Probab. Letters, 33: 321–331.  [Google Scholar] and the Lagrange multiplier test are carried out.     

Local influence diagnostics for generalized linear mixed models with overdispersion

Since the seminal paper by Cook and Weisberg [9 R.D. Cook and S. Weisberg, Residuals and Influence in Regression, Chapman &; Hall, London, 1982. [Google Scholar]], local influence, next to case deletion, has gained popularity as a tool to detect influential subjects and measurements for a variety of statistical models. For the linear mixed model the approach leads to easily interpretable and computationally convenient expressions, not only highlighting influential subjects, but also which aspect of their profile leads to undue influence on the model's fit [17 E. Lesaffre and G. Verbeke, Local influence in linear mixed models, Biometrics 54 (1998), pp. 570–582. doi: 10.2307/3109764[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]]. Ouwens et al. [24 M.J.N.M. Ouwens, F.E.S. Tan, and M.P.F. Berger, Local influence to detect influential data structures for generalized linear mixed models, Biometrics 57 (2001), pp. 1166–1172. doi: 10.1111/j.0006-341X.2001.01166.x[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]] applied the method to the Poisson-normal generalized linear mixed model (GLMM). Given the model's nonlinear structure, these authors did not derive interpretable components but rather focused on a graphical depiction of influence. In this paper, we consider GLMMs for binary, count, and time-to-event data, with the additional feature of accommodating overdispersion whenever necessary. For each situation, three approaches are considered, based on: (1) purely numerical derivations; (2) using a closed-form expression of the marginal likelihood function; and (3) using an integral representation of this likelihood. Unlike when case deletion is used, this leads to interpretable components, allowing not only to identify influential subjects, but also to study the cause thereof. The methodology is illustrated in case studies that range over the three data types mentioned.     

Upper Bounds for the Ruin Probabilities of the Entrance-Based Risk Model

Li et al. (2005 Li , Z. , Zhu , J. , Chen , F. ( 2005 ). Study of a risk model based on the entrance process . Statist. Probab. Lett. 72 ( 1 ): 1 – 10 .[Crossref], [Web of Science ®] , [Google Scholar]) proposed a risk model based on the entrance process and studied the asymptotic behavior of the surplus when time goes to infinity. This article considers the ruin problem in that model. Some simple characteristics (stochastic intensity, compensator, mean process, etc.) of the risk process and other related processes are also considered. Under small claim condition, exponential upper bounds for the ruin probability are obtained.     

Buffered Autoregressive Models With Conditional Heteroscedasticity: An Application to Exchange Rates

This article introduces a new model called the buffered autoregressive model with generalized autoregressive conditional heteroscedasticity (BAR-GARCH). The proposed model, as an extension of the BAR model in Li et al. (2015 Li, G.D., Guan, B., Li, W.K., and Yu, P. L.H. (2015), “Hysteretic Autoregressive Time Series Models,” Biometrika, 102, 717–723.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), can capture the buffering phenomena of time series in both the conditional mean and variance. Thus, it provides us a new way to study the nonlinearity of time series. Compared with the existing AR-GARCH and threshold AR-GARCH models, an application to several exchange rates highlights the importance of the BAR-GARCH model.     

Examining the interrelation dynamics between option and stock markets using the Markov-switching vector error correction model

This study examines the dynamics of the interrelation between option and stock markets using the Markov-switching vector error correction model. Specifically, we calculate the implied stock prices from the Black–Scholes 6 Black, F. and Scholes, M. 1973. The pricing of options and corporate liabilities. J. Polit. Econ., 81: 637–659. [Crossref], [Web of Science ®] [Google Scholar] model and establish a statistic framework in which the parameter of the price discrepancy between the observed and implied prices switches according to the phase of the volatility regime. The model is tested in the US S&P 500 stock market. The empirical findings of this work are consistent with the following notions. First, while option markets react more quickly to the newest stock–option disequilibrium shocks than spot markets, as found by earlier studies, we further indicate that the price adjustment process occurring in option markets is pronounced when the high variance condition is concerned, but less so during the stable period. Second, the degree of the co-movement between the observed and implied prices is significantly reduced during the high variance state. Last, the lagged price deviation between the observed and implied prices functions as an indicator of the variance-turning process.     

A new cure rate model based on the Yule–Simon distribution with application to a melanoma data set

In this paper, a new survival cure rate model is introduced considering the Yule–Simon distribution [12 H.A. Simon, On a class of skew distribution functions, Biometrika 42 (1955), pp. 425–440.[Crossref], [Web of Science ®] , [Google Scholar]] to model the number of concurrent causes. We study some properties of this distribution and the model arising when the distribution of the competing causes is the Weibull model. We call this distribution the Weibull–Yule–Simon distribution. Maximum likelihood estimation is conducted for model parameters. A small scale simulation study is conducted indicating satisfactory parameter recovery by the estimation approach. Results are applied to a real data set (melanoma) illustrating the fact that the model proposed can outperform traditional alternative models in terms of model fitting.     

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.     

Interval Estimation by Frequentist Model Averaging

An important contribution to the literature on frequentist model averaging (FMA) is the work of Hjort and Claeskens (2003 Hjort , N. L. , Claeskens , G. ( 2003 ). Frequestist model average estimators . J. Amer. Statist. Assoc. 98 : 879 – 899 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), who developed an asymptotic theory for frequentist model averaging in parametric models based on a local mis-specification framework. They also proposed a simple method for constructing confidence intervals of the unknown parameters. This article shows that the confidence intervals based on the FMA estimator suggested by Hjort and Claeskens (2003 Hjort , N. L. , Claeskens , G. ( 2003 ). Frequestist model average estimators . J. Amer. Statist. Assoc. 98 : 879 – 899 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) are asymptotically equivalent to that obtained from the full model under both parametric and the varying-coefficient partially linear models. Thus, as long as interval estimation rather than point estimation is concerned, the confidence interval based on the full model already fulfills the objective and model averaging provides no additional useful information.