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In this paper, Bayesian estimates are derived for the location and scale parameters of the Laplace distribution based on complete, Type-I, and Type-II censored samples under different prior settings. Subsequently, Bayesian point and interval estimates, as well as the associated statistical inference, are discussed in detail. The developed methods are then applied to two real data sets for illustrative purposes. Moreover, a detailed Monte Carlo simulation study is carried out for evaluating the performance of the inferential methods developed here. Finally, we provide a brief discussion of the established results to demonstrate their practical utility and present some associated problems of further interest. Overall, this study fills an existing gap in the development of Bayesian inferential techniques for the parameters of the two-parameter Laplace distribution, making this research innovative and offering more investigative implications. It showcases the potential for broader methodological applications of Bayesian inference for complex real-world data sets, especially in scenarios involving different forms of censoring. This research provides a critical tool for statistical analysis in different fields such as engineering and finance, where the Laplace distribution is frequently adopted as a fundamental model. [ABSTRACT FROM AUTHOR]

Applications of circular regression models are ubiquitous in many disciplines, particularly in meteorology, biology and geology. In circular regression models, variable selection problem continues to be a remarkable open question. In this paper, we address variable selection in linear-circular regression models where uni-variate linear dependent and a mixed set of circular and linear independent variables constitute the data set. We consider Bayesian lasso which is a popular choice for variable selection in classical linear regression models. We show that Bayesian lasso in linear-circular regression models is not able to produce robust inference as the coefficient estimates are sensitive to the choice of hyper-prior setting for the tuning parameter. To eradicate the problem, we propose a robustified Bayesian lasso that is based on an empirical Bayes (EB) type methodology to construct a hyper-prior for the tuning parameter while using Gibbs Sampling. This hyper-prior construction is computationally more feasible than the hyper-priors that are based on correlation measures. We show in a comprehensive simulation study that Bayesian lasso with EB-GS hyper-prior leads to a more robust inference. Overall, the method offers an efficient Bayesian lasso for variable selection in linear-circular regression while reducing model complexity. [ABSTRACT FROM AUTHOR]

This paper presents a Bayesian analysis of linear mixed models for quantile regression using a modified Cholesky decomposition for the covariance matrix of random effects and an asymmetric Laplace distribution for the error distribution. We consider several novel Bayesian shrinkage approaches for both fixed and random effects in a linear mixed quantile model using extended L 1 penalties. To improve mixing of the Markov chains, a simple and efficient partially collapsed Gibbs sampling algorithm is developed for posterior inference. We also extend the framework to a Bayesian mixed expectile model and develop a Metropolis–Hastings acceptance–rejection (MHAR) algorithm using proposal densities based on iteratively weighted least squares estimation. The proposed approach is then illustrated via both simulated and real data examples. Results indicate that the proposed approach performs very well in comparison to the other approaches. [ABSTRACT FROM AUTHOR]

According to the Atlas of Human Development in Brazil, the income dimension of Municipal Human Development Index (MHDI-I) is an indicator that shows the population's ability in a municipality to ensure a minimum standard of living to provide their basic needs, such as water, food and shelter. In public policy, one of the research objectives is to identify social and economic variables that are associated with this index. Due to the income inequality, evaluate these associations in quantiles, instead of the mean, could be more interest. Thus, in this paper, we develop a Bayesian variable selection in quantile regression models with hierarchical random effects. In particular, we assume a likelihood function based on the Generalized Asymmetric Laplace distribution, and a spike-and-slab prior is used to perform variable selection. The Generalized Asymmetric Laplace distribution is a more general alternative than the Asymmetric Laplace one, which is a common approach used in quantile regression under the Bayesian paradigm. The performance of the proposed method is evaluated via a comprehensive simulation study, and it is applied to the MHDI-I from municipalities located in the state of Rio de Janeiro. [ABSTRACT FROM AUTHOR]

Time lag effect exists widely in the course of economic operation. Some economic variables are affected not only by various factors in the current period but also by various factors in the past and even their own past values. As a class of dynamical models, autoregressive distributed lag (ARDL) models are frequently used to conduct dynamic regression analysis. In this paper, we are interested in the quantile regression (QR) modeling of the ARDL model in a dynamic framework. By combining the working likelihood of asymmetric Laplace distribution (ALD) with the expectation–maximization (EM) algorithm into the considered ARDL model, the iterative weighted least square estimators (IWLSE) are derived. Some Monte Carlo simulations are implemented to evaluate the performance of the proposed estimation method. A dataset of the consumption of electricity by residential customers is analyzed to illustrate the application. [ABSTRACT FROM AUTHOR]

Conditional risk measuring plays an important role in financial regulation and depends on volatility estimation. A new class of parameter models called Generalized Autoregressive Score (GAS) model has been successfully applied for different error's densities and for different problems of time series prediction in particular for volatility modeling and VaR estimation. To improve the estimating accuracy of the GAS model, this study proposed a semi-parametric method, LS-SVR and FS-LS-SVR applied to the GAS model to estimate the conditional VaR. In particular, we fit the GAS(1,1) model to the return series using three different distributions. Then, LS-SVR and FS-LS-SVR approximate the GAS(1,1) model. An empirical research was performed to illustrate the effectiveness of the proposed method. More precisely, the experimental results from four stock indexes returns suggest that using hybrid models, GAS-LS-SVR and GAS-FS-LS-SVR provides improved performances in the VaR estimation. [ABSTRACT FROM AUTHOR]

In this paper, we develop a conditional model for analyzing mixed bivariate continuous and ordinal longitudinal responses. We propose a quantile regression model with random effects for analyzing continuous responses. For this purpose, an Asymmetric Laplace Distribution (ALD) is allocated for continuous response given random effects. For modeling ordinal responses, a cumulative logit model is used, via specifying a latent variable model, with considering other random effects. Therefore, the intra-association between continuous and ordinal responses is taken into account using their own exclusive random effects. But, the inter-association between two mixed responses is taken into account by adding a continuous response term in the ordinal model. We use a Bayesian approach via Markov chain Monte Carlo method for analyzing the proposed conditional model and to estimate unknown parameters, a Gibbs sampler algorithm is used. Moreover, we illustrate an application of the proposed model using a part of the British Household Panel Survey data set. The results of data analysis show that gender, age, marital status, educational level and the amount of money spent on leisure have significant effects on annual income. Also, the associated parameter is significant in using the best fitting proposed conditional model, thus it should be employed rather than analyzing separate models. [ABSTRACT FROM AUTHOR]

We often rely on the likelihood to obtain estimates of regression parameters but it is not readily available for generalized linear mixed models (GLMMs). Inferences for the regression coefficients and the covariance parameters are key in these models. We presented alternative approaches for analyzing binary data from a hierarchical structure that do not rely on any distributional assumptions: a generalized quasi-likelihood (GQL) approach and a generalized method of moments (GMM) approach. These are alternative approaches to the typical maximum-likelihood approximation approach in Statistical Analysis System (SAS) such as Laplace approximation (LAP). We examined and compared the performance of GQL and GMM approaches with multiple random effects to the LAP approach as used in PROC GLIMMIX, SAS. The GQL approach tends to produce unbiased estimates, whereas the LAP approach can lead to highly biased estimates for certain scenarios. The GQL approach produces more accurate estimates on both the regression coefficients and the covariance parameters with smaller standard errors as compared to the GMM approach. We found that both GQL and GMM approaches are less likely to result in non-convergence as opposed to the LAP approach. A simulation study was conducted and a numerical example was presented for illustrative purposes. [ABSTRACT FROM PUBLISHER]

The multi-cycle organization of modern university systems stimulates the interest in studying the progression to higher level degree courses during the academic career. In particular, after the achievement of the first level qualification (Bachelor degree), students have to decide whether to continue their university studies, by enrolling in a second level (Master) programme, or to conclude their training experience. In this work we propose a binary quantile regression (BQR) approach to analyse the Bachelor-to-Master transition phenomenon with the adoption of the Bayesian inferential perspective. In addition to the traditional predictors of academic outcomes, such as the personal characteristics and the field of study, different aspects of student's performance are considered. Moreover, the role of a new contextual variable, representing the type of university regulations experienced during the academic path, is investigated. The utility of the Bayesian BQR to characterize the non-continuation decision after the first cycle studies is illustrated with an application to administrative data of Bachelor graduates at the School of Economics of Sapienza University of Rome. The method favourably compares with more conventional model specifications concerning the conditional mean of the binary response. [ABSTRACT FROM PUBLISHER]

Generalized linear models (GLMs) with error-in-covariates are useful in epidemiological research due to the ubiquity of non-normal response variables and inaccurate measurements. The link function in GLMs is chosen by the user depending on the type of response variable, frequently the canonical link function. When covariates are measured with error, incorrect inference can be made, compounded by incorrect choice of link function. In this article we propose three flexible approaches for handling error-in-covariates and estimating an unknown link simultaneously. The first approach uses a fully Bayesian (FB) hierarchical framework, treating the unobserved covariate as a latent variable to be integrated over. The second and third are approximate Bayesian approach which use a Laplace approximation to marginalize the variables measured with error out of the likelihood. Our simulation results show support that the FB approach is often a better choice than the approximate Bayesian approaches for adjusting for measurement error, particularly when the measurement error distribution is misspecified. These approaches are demonstrated on an application with binary response. [ABSTRACT FROM AUTHOR]

Conventional methods apply symmetric prior distributions such as a normal distribution or a Laplace distribution for regression coefficients, which may be suitable for median regression and exhibit no robustness to outliers. This work develops a quantile regression on linear panel data model without heterogeneity from a Bayesian point of view, i.e. upon a location-scale mixture representation of the asymmetric Laplace error distribution, and provides how the posterior distribution is summarized using Markov chain Monte Carlo methods. Applying this approach to the 1970 British Cohort Study (BCS) data, it finds that a different maternal health problem has different influence on child's worrying status at different quantiles. In addition, applying stochastic search variable selection for maternal health problems to the 1970 BCS data, it finds that maternal nervous breakdown, among the 25 maternal health problems, contributes most to influence the child's worrying status. [ABSTRACT FROM PUBLISHER]

Three new weighted rank correlation coefficients are proposed which are sensitive to both agreement on top and bottom rankings. The first one is based on the weighted rank correlation coefficient proposed by Maturi and Abdelfattah [13], the second and the third are based on the order statistics and the quantiles of the Laplace distribution, respectively. The limiting distributions of the new correlation coefficients under the null hypothesis of no association between the rankings are presented, and a summary of the exact and approximate quantiles for these coefficients is provided.Asimulation study is performed to compare the performance of Kendall's tau, Spearman's rho, and the new weighted rank correlation coefficients in detecting the agreement on the top and the bottom rankings simultaneously. Finally, examples are given for illustration purposes, including a real data set from financial market indices. [ABSTRACT FROM AUTHOR]

Mixture of linear regression models provide a popular treatment for modeling nonlinear regression relationship. The traditional estimation of mixture of regression models is based on Gaussian error assumption. It is well known that such assumption is sensitive to outliers and extreme values. To overcome this issue, a new class of finite mixture of quantile regressions (FMQR) is proposed in this article. Compared with the existing Gaussian mixture regression models, the proposed FMQR model can provide a complete specification on the conditional distribution of response variable for each component. From the likelihood point of view, the FMQR model is equivalent to the finite mixture of regression models based on errors following asymmetric Laplace distribution (ALD), which can be regarded as an extension to the traditional mixture of regression models with normal error terms. An EM algorithm is proposed to obtain the parameter estimates of the FMQR model by combining a hierarchical representation of the ALD. Finally, the iterated weighted least square estimation for each mixture component of the FMQR model is derived. Simulation studies are conducted to illustrate the finite sample performance of the estimation procedure. Analysis of an aphid data set is used to illustrate our methodologies. [ABSTRACT FROM PUBLISHER]

In this paper, we introduce a general goodness of fit test based on Phi-divergence. Consistency of the proposed test is established. We then study some special cases of tests for normal, exponential, uniform and Laplace distributions. Through Monte Carlo simulations, the power values of the proposed tests are compared with some known competing tests under various alternatives. Finally, some numerical examples are presented to illustrate the proposed procedure. [ABSTRACT FROM PUBLISHER]

The statistical difference among massive data sets or signals is of interest to many diverse fields including neurophysiology, imaging, engineering, and other related fields. However, such data often have nonlinear curves, depending on spatial patterns, and have non-white noise that leads to difficulties in testing the significant differences between them. In this paper, we propose an adaptive Bayes sum test that can test the significance between two nonlinear curves by taking into account spatial dependence and by reducing the effect of non-white noise. Our approach is developed by adapting the Bayes sum test statistic by Hart [13]. The spatial pattern is treated through Fourier transformation. Resampling techniques are employed to construct the empirical distribution of test statistic to reduce the effect of non-white noise. A simulation study suggests that our approach performs better than the alternative method, the adaptive Neyman test by Fan and Lin [9]. The usefulness of our approach is demonstrated with an application in the identification of electronic chips as well as an application to test the change of pattern of precipitations. [ABSTRACT FROM PUBLISHER]

Applications of circular regression models are ubiquitous in many disciplines, particularly in meteorology, biology and geology. In circular regression models, variable selection problem continues to be a remarkable open question. In this paper, we address variable selection in linear-circular regression models where uni-variate linear dependent and a mixed set of circular and linear independent variables constitute the data set. We consider Bayesian lasso which is a popular choice for variable selection in classical linear regression models. We show that Bayesian lasso in linear-circular regression models is not able to produce robust inference as the coefficient estimates are sensitive to the choice of hyper-prior setting for the tuning parameter. To eradicate the problem, we propose a robustified Bayesian lasso that is based on an empirical Bayes (EB) type methodology to construct a hyper-prior for the tuning parameter while using Gibbs Sampling. This hyper-prior construction is computationally more feasible than the hyper-priors that are based on correlation measures. We show in a comprehensive simulation study that Bayesian lasso with EB-GS hyper-prior leads to a more robust inference. Overall, the method offers an efficient Bayesian lasso for variable selection in linear-circular regression while reducing model complexity., Competing Interests: No potential conflict of interest was reported by the author(s)., (© 2022 Informa UK Limited, trading as Taylor & Francis Group.)

In a microarray experiment, intensity measurements tend to vary due to various systematic and random effects, which enter at the different stages of the measurement process. Common test statistics do not take these effects into account. An alternative is to use, for example, ANOVA models. In many cases, we can, however, not make the assumption of normally distributed error terms. Purdom and Holmes [6] have concluded that the distribution of microarray intensity measurements can often be better approximated by a Laplace distribution. In this paper, we consider the analysis of microarray data by using ANOVA models under the assumption of Laplace-distributed error terms. We explain the methodology and discuss problems related to fitting of this type of models. In addition to evaluating the models using several real-life microarray experiments, we conduct a simulation study to investigate different aspects of the models in detail. We find that, while the normal model is less sensitive to model misspecifications, the Laplace model has more power when the data are truly Laplace distributed. However, in the latter situation, neither of the models is able to control the false discovery rate at the pre-specified significance level. This problem is most likely related to sample size issues. [ABSTRACT FROM AUTHOR]