Computationally and statistically efficient model fitting techniques

A significant challenge in fitting metamodels of large-scale simulations with sufficient accuracy is in the computational time required for rigorous statistical validation. This paper addresses the statistical computation issues associated with the Bootstrap and modified PRESS statistic, which yield key metrics for error measurements in metamodelling validation. Experimentation is performed on different programming languages, namely, MATLAB, R, and Python, and implemented on different computing architectures including traditional multicore personal computers and high-power clusters with parallel computing capabilities. This study yields insight into the effect that programming languages and computing architecture have on the computational time for simulation metamodel validation. The experimentation is performed across two scenarios with varying complexity.     

Quantile regression for robust estimation and variable selection in partially linear varying-coefficient models

In this paper, we develop a new estimation procedure based on quantile regression for semiparametric partially linear varying-coefficient models. The proposed estimation approach is empirically shown to be much more efficient than the popular least squares estimation method for non-normal error distributions, and almost not lose any efficiency for normal errors. Asymptotic normalities of the proposed estimators for both the parametric and nonparametric parts are established. To achieve sparsity when there exist irrelevant variables in the model, two variable selection procedures based on adaptive penalty are developed to select important parametric covariates as well as significant nonparametric functions. Moreover, both these two variable selection procedures are demonstrated to enjoy the oracle property under some regularity conditions. Some Monte Carlo simulations are conducted to assess the finite sample performance of the proposed estimators, and a real-data example is used to illustrate the application of the proposed methods.     

Estimation of structural mean breaks for long-memory data sets

In long-memory data sets such as the realized volatilities of financial assets, a sequential test is developed for the detection of structural mean breaks. The long memory, if any, is adjusted by fitting an HAR (heterogeneous autoregressive) model to the data sets and taking the residuals. Our test consists of applying the sequential test of Bai and Perron [Estimating and testing linear models with multiple structural changes. Econometrica. 1998;66:47–78] to the residuals. The large-sample validity of the proposed test is investigated in terms of the consistency of the estimated number of breaks and the asymptotic null distribution of the proposed test. A finite-sample Monte-Carlo experiment reveals that the proposed test tends to produce an unbiased break time estimate, while the usual sequential test of Bai and Perron tends to produce biased break times in the case of long memory. The experiment also reveals that the proposed test has a more stable size than the Bai and Perron test. The proposed test is applied to two realized volatility data sets of the S&P index and the Korea won-US dollar exchange rate for the past 7 years and finds 2 or 3 breaks, while the Bai and Perron test finds 8 or more breaks.     

On the asymptotic normality of the R-estimators of the slope parameters of simple linear regression models with associated errors

ABSTRACT

The purpose of this paper is to prove, under mild conditions, the asymptotic normality of the rank estimator of the slope parameter of a simple linear regression model with stationary associated errors. This result follows from a uniform linearity property for linear rank statistics that we establish under general conditions on the dependence of the errors. We prove also a tightness criterion for weighted empirical process constructed from associated triangular arrays. This criterion is needed for the proofs which are based on that of Koul [Behavior of robust estimators in the regression model with dependent errors. Ann Stat. 1977;5(4):681–699] and of Louhichi [Louhichi S. Weak convergence for empirical processes of associated sequences. Ann Inst Henri Poincaré Probabilités Statist. 2000;36(5):547–567].     

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.     

Flexible objective Bayesian linear regression with applications in survival analysis

We study objective Bayesian inference for linear regression models with residual errors distributed according to the class of two-piece scale mixtures of normal distributions. These models allow for capturing departures from the usual assumption of normality of the errors in terms of heavy tails, asymmetry, and certain types of heteroscedasticity. We propose a general non-informative, scale-invariant, prior structure and provide sufficient conditions for the propriety of the posterior distribution of the model parameters, which cover cases when the response variables are censored. These results allow us to apply the proposed models in the context of survival analysis. This paper represents an extension to the Bayesian framework of the models proposed in [16]. We present a simulation study that shows good frequentist properties of the posterior credible intervals as well as point estimators associated to the proposed priors. We illustrate the performance of these models with real data in the context of survival analysis of cancer patients.     

Bayesian elastic net single index quantile regression

Single index model conditional quantile regression is proposed in order to overcome the dimensionality problem in nonparametric quantile regression. In the proposed method, the Bayesian elastic net is suggested for single index quantile regression for estimation and variables selection. The Gaussian process prior is considered for unknown link function and a Gibbs sampler algorithm is adopted for posterior inference. The results of the simulation studies and numerical example indicate that our propose method, BENSIQReg, offers substantial improvements over two existing methods, SIQReg and BSIQReg. The BENSIQReg has consistently show a good convergent property, has the least value of median of mean absolute deviations and smallest standard deviations, compared to the other two methods.     

Local influence in seemingly unrelated regression model with ridge estimate

Local influence is a well-known method for identifying the influential observations in a dataset and commonly needed in a statistical analysis. In this paper, we study the local influence on the parameters of interest in the seemingly unrelated regression model with ridge estimation, when there exists collinearity among the explanatory variables. We examine two types of perturbation schemes to identify influential observations: the perturbation of variance and the perturbation of individual explanatory variables. Finally, the efficacy of our proposed method is illustrated by analyzing [13 A. Munnell, Why has productivity declined? Productivity and public investment, New Engl. Econ. Rev. (1990), pp. 3–22. [Google Scholar]] productivity dataset.     

A Bayesian model for multiple change point to extremes,with application to environmental and financial data

Abrupt changes often occur for environmental and financial time series. Most often, these changes are due to human intervention. Change point analysis is a statistical tool used to analyze sudden changes in observations along the time series. In this paper, we propose a Bayesian model for extreme values for environmental and economic datasets that present a typical change point behavior. The model proposed in this paper addresses the situation in which more than one change point can occur in a time series. By analyzing maxima, the distribution of each regime is a generalized extreme value distribution. In this model, the change points are unknown and considered parameters to be estimated. Simulations of extremes with two change points showed that the proposed algorithm can recover the true values of the parameters, in addition to detecting the true change points in different configurations. Also, the number of change points was a problem to be considered, and the Bayesian estimation can correctly identify the correct number of change points for each application. Environmental and financial data were analyzed and results showed the importance of considering the change point in the data and revealed that this change of regime brought about an increase in the return levels, increasing the number of floods in cities around the rivers. Stock market levels showed the necessity of a model with three different regimes.