Generalised Rank Regression Estimator with Standard Error Adjusted Lasso

One of the standard variable selection procedures in multiple linear regression is to use a penalisation technique in least‐squares (LS) analysis. In this setting, many different types of penalties have been introduced to achieve variable selection. It is well known that LS analysis is sensitive to outliers, and consequently outliers can present serious problems for the classical variable selection procedures. Since rank‐based procedures have desirable robustness properties compared to LS procedures, we propose a rank‐based adaptive lasso‐type penalised regression estimator and a corresponding variable selection procedure for linear regression models. The proposed estimator and variable selection procedure are robust against outliers in both response and predictor space. Furthermore, since rank regression can yield unstable estimators in the presence of multicollinearity, in order to provide inference that is robust against multicollinearity, we adjust the penalty term in the adaptive lasso function by incorporating the standard errors of the rank estimator. The theoretical properties of the proposed procedures are established and their performances are investigated by means of simulations. Finally, the estimator and variable selection procedure are applied to the Plasma Beta‐Carotene Level data set.     

Semi-doubly optimal concentric circles fitting with presence of heteroscedasticity

Previous studies focus on homogeneous and isotropic assumptions about the noisy data. Many methods have been developed recently for fitting concentric circles to data. In this paper, these statistical assumptions have been relaxed. To the best of our knowledge, only one iterative method has been recently developed. Due to its complexity, no such algorithm is available to compute the reliable maximum likelihood estimator (MLE). Accordingly, we have developed four new methods that outperform the existing methods including the orthogonal distance regression (ODR). We also discuss which of these methods is superior according to the four principles: statistical efficiency, accuracy, robustness, and computational efficiency. Numerical experiments on synthetic and real images have been conducted to validate our findings.     

Multivariate log-skewed distributions with normal kernel and their applications

We introduce two classes of multivariate log-skewed distributions with normal kernel: the log canonical fundamental skew-normal (log-CFUSN) and the log unified skew-normal. We also discuss some properties of the log-CFUSN family of distributions. These new classes of log-skewed distributions include the log-normal and multivariate log-skew normal families as particular cases. We discuss some issues related to Bayesian inference in the log-CFUSN family of distributions, mainly we focus on how to model the prior uncertainty about the skewing parameter. Based on the stochastic representation of the log-CFUSN family, we propose a data augmentation strategy for sampling from the posterior distributions. This proposed family is used to analyse the US national monthly precipitation data. We conclude that a high-dimensional skewing function lead to a better model fit.     

A Method to Handle Zero Counts in the Multinomial Model

In the context of an objective Bayesian approach to the multinomial model, Dirichlet(a, …, a) priors with a < 1 have previously been shown to be inadequate in the presence of zero counts, suggesting that the uniform prior (a = 1) is the preferred candidate. In the presence of many zero counts, however, this prior may not be satisfactory either. A model selection approach is proposed, allowing for the possibility of zero parameters corresponding to zero count categories. This approach results in a posterior mixture of Dirichlet distributions and marginal mixtures of beta distributions, which seem to avoid the problems that potentially result from the various proposed Dirichlet priors, in particular in the context of extreme data with zero counts.     

Modern likelihood inference for the maximum/minimum of a bivariate normal vector

ABSTRACT

We consider the use of modern likelihood asymptotics in the construction of confidence intervals for the parameter which determines the skewness of the distribution of the maximum/minimum of an exchangeable bivariate normal random vector. Simulation studies were conducted to investigate the accuracy of the proposed methods and to compare them to available alternatives. Accuracy is evaluated in terms of both coverage probability and expected length of the interval. We furthermore illustrate the suitability of our proposals by means of two data sets, consisting of, respectively, measurements taken on the brains of 10 mono-zygotic twins and measurements of mineral content of bones in the dominant and non-dominant arms for 25 elderly women.     

Confidence distributions applied to propagating uncertainty to inference based on estimating the local false discovery rate: A fiducial continuum from confidence sets to empirical Bayes set estimates as the number of comparisons increases

Empirical Bayes estimates of the local false discovery rate can reflect uncertainty about the estimated prior by supplementing their Bayesian posterior probabilities with confidence levels as posterior probabilities. This use of coherent fiducial inference with hierarchical models generates set estimators that propagate uncertainty to varying degrees. Some of the set estimates approach estimates from plug-in empirical Bayes methods for high numbers of comparisons and can come close to the usual confidence sets given a sufficiently low number of comparisons.     

Choosing Prior Hyperparameters: With Applications to Time-Varying Parameter Models

Time-varying parameter models with stochastic volatility are widely used to study macroeconomic and financial data. These models are almost exclusively estimated using Bayesian methods. A common practice is to focus on prior distributions that themselves depend on relatively few hyperparameters such as the scaling factor for the prior covariance matrix of the residuals governing time variation in the parameters. The choice of these hyperparameters is crucial because their influence is sizeable for standard sample sizes. In this article, we treat the hyperparameters as part of a hierarchical model and propose a fast, tractable, easy-to-implement, and fully Bayesian approach to estimate those hyperparameters jointly with all other parameters in the model. We show via Monte Carlo simulations that, in this class of models, our approach can drastically improve on using fixed hyperparameters previously proposed in the literature. Supplementary materials for this article are available online.     

Evaluating the causal economic impacts of transport investments: evidence from the Madrid–Barcelona high speed rail corridor

This paper evaluates economic impacts arising from the introduction of high-speed rail (HSR) between Madrid and Barcelona. Using difference-in-differences estimation we estimate an average treatment effect for provinces with stops on the HSR line of 2.4% for economic output, 3.3% for numbers of firms, and 1.1% for labour productivity. We complement our DID results with a synthetic control analysis for Lleida and Tarragona, two provinces that we argue were assigned HSR stations largely due to their incidental location. We find that both the number of firms and labour productivity are substantially higher in these provinces than in their synthetic counterparts.     

Estimation and Properties of a Time-Varying EGARCH(1,1) in Mean Model

Time-varying GARCH-M models are commonly employed in econometrics and financial economics. Yet the recursive nature of the conditional variance makes likelihood analysis of these models computationally infeasible. This article outlines the issues and suggests to employ a Markov chain Monte Carlo algorithm which allows the calculation of a classical estimator via the simulated EM algorithm or a simulated Bayesian solution in only O(T) computational operations, where T is the sample size. Furthermore, the theoretical dynamic properties of a time-varying-parameter EGARCH(1,1)-M are derived. We discuss them and apply the suggested Bayesian estimation to three major stock markets.