Article
Computer Science, Interdisciplinary Applications
Hanjun Yu, Lichao Yu
Summary: We propose a flexible Bayesian quantile regression method for analyzing longitudinal data based on a class of parametric nonlinear mixed effects models using the generalized asymmetric Laplace distribution. This method exhibits more flexibility than commonly used asymmetric Laplace distribution in quantile regression, allowing for better characterization of skewness, mode, and tail behavior in the data. We derive an efficient Markov chain Monte Carlo procedure based on the adaptive random walk Metropolis-within-Gibbs sampling algorithm for posterior inference. Simulation studies and empirical analysis demonstrate that the proposed method provides more accurate parameter estimation and better model fit compared to existing methods.
JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION
(2023)
Article
Computer Science, Interdisciplinary Applications
Kai Y. K. Wang, Cathy W. S. Chen, Mike K. P. So
Summary: The Fama-French three-factor model improves the capital asset pricing model by including size risk and value risk factors as market risk factors. This study proposes a quantile Fama-French three-factor model with GARCH-type dynamics, leptokurtosis, and skewness through asymmetric Student t errors to address the limitations of existing models. The proposed model allows for investigating the effects of daily volatility and market risk factors under different market conditions represented by quantile levels.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2023)
Article
Automation & Control Systems
Chao Xu, Xianqiang Yang, Miao Yu
Summary: This paper focuses on the robust parameters estimation algorithm for linear parameters varying (LPV) models, extending robustness to both symmetric and asymmetric noise by employing asymmetric Laplace distribution and introducing a shifted parameter for regression, solving the robust parameters estimation problem in the general Expectation Maximization algorithm framework. The proposed algorithm's advantage is demonstrated through a numerical simulation example.
MEASUREMENT & CONTROL
(2021)
Article
Multidisciplinary Sciences
Fengkai Yang
Summary: We propose a robust change-point estimation procedure based on a quantile regression model with asymmetric Laplace error distribution and develop a non-iterative sampling algorithm from a Bayesian perspective. The algorithm can generate independently and identically distributed samples approximately from the posterior distribution of the position of the change-point, which can be used for statistical inferences straightforwardly. The procedure combines the robustness of quantile regression and the computational efficiency of the non-iterative sampling algorithm. A simulation study is conducted to illustrate the performance of the procedure with satisfying findings, and finally, real data is analyzed to show the usefulness of the algorithm by comparison with the usual change-point detection method based on normal regression.
Article
Engineering, Industrial
Shijuan Yang, Jianjun Wang, Yiliu Tu, Yunxia Han, Xiaolei Ren, Chunfeng Ding, Xiaoying Chen
Summary: This paper proposes a robust multi-response surface modelling and optimisation method based on Bayesian quantile regression, which effectively addresses the influence of model parameter uncertainty and outliers on the optimization results.
INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH
(2023)
Article
Infectious Diseases
Ashenafi A. Yirga, Sileshi F. Melesse, Henry G. Mwambi, Dawit G. Ayele
Summary: This study uses a quantile mixed-effects model to analyze the CD4 cell count of HIV-infected patients. The results indicate that baseline BMI, baseline viral load, and post-HAART initiation are significant factors affecting CD4 count.
BMC INFECTIOUS DISEASES
(2022)
Article
Statistics & Probability
Jorge Castillo-Mateo, Jesus Asin, Ana C. Cebrian, Alan E. Gelfand, Jesus Abaurrea
Summary: Regression is the most commonly used modeling tool in statistics, and quantile regression provides enhanced capabilities in regression analysis. This study examines the spatiotemporal evolution of daily maximum temperature, particularly extreme heat, using 60 years of data from Aragon, Spain. The research utilizes time-series and spatial referencing to model the data and calculate quantiles for each day within the study region.
ANNALS OF APPLIED STATISTICS
(2023)
Article
Economics
Zijian Zeng, Meng Li
Summary: A Bayesian median autoregressive model was developed for time series forecasting, utilizing time-varying quantile regression at the median and a Laplace error instead of Gaussian error. Model parameters were estimated using Markov chain Monte Carlo, with Bayesian model averaging and model selection used to address model uncertainty. The methods showed favorable predictive performance in real data applications.
INTERNATIONAL JOURNAL OF FORECASTING
(2021)
Article
Ecology
Sam Nicol, Marie-Josee Cros, Nathalie Peyrard, Regis Sabbadin, Ronan Trepos, Richard A. Fuller, Bradley K. Woodworth
Summary: This article introduces the concept of FlywayNet, a discrete network model based on observed count data, to determine the structure of migratory networks in birds. By modeling noisy observations and flexible stopover durations using interacting hidden semi-Markov models, this approach advances previous studies and provides a flexible framework for studying migratory networks in birds and other organisms.
METHODS IN ECOLOGY AND EVOLUTION
(2023)
Article
Statistics & Probability
Suk Joo Bae, Byeong Min Mun, Xiaoyan Zhu
Summary: In this study, we propose a reliability model based on a proportional intensity model with frailty for left-truncated and right-censored recurrent failure data from multiple repairable systems. The model explicitly accounts for unobserved heterogeneity among the systems and incorporates covariates to consider heterogeneity between different operating conditions. We use a Monte Carlo expectation maximization algorithm to estimate the model parameters and construct confidence intervals. A real-world example and simulation studies demonstrate the importance of this model for reliability prediction in multiple repairable systems.
Article
Computer Science, Theory & Methods
Luca Merlo, Antonello Maruotti, Lea Petrella, Antonio Punzo
Summary: This paper develops a new method for jointly estimating multiple quantiles of multivariate time series. The method considers the correlation structure among outcomes and models the unobserved serial heterogeneity using a hidden semi-Markov chain. Inference is carried out using an efficient algorithm that avoids parametric assumptions about the states' sojourn distributions.
STATISTICS AND COMPUTING
(2022)
Article
Automation & Control Systems
Xuehui Ma, Fucai Qian, Shiliang Zhang, Li Wu
Summary: This paper proposes an adaptive quantile control method for stochastic systems with sharp and thick tail noise distributions, utilizing Bayesian quantile sum estimator for online parameter estimation and real-time control. Compared with other controllers, this method shows higher effectiveness.
Article
Computer Science, Interdisciplinary Applications
Sanket Jantre
Summary: This work introduces a Bayesian quantile regression modelling framework for the analysis of longitudinal count data. The response variable in this model is not continuous, so an artificial smoothing of counts is incorporated. The Bayesian implementation uses the normal-exponential mixture representation of the asymmetric Laplace distribution for the response variable. An efficient Gibbs sampling algorithm is derived for fitting the model to the data. The model is validated through simulation studies and an application in neurology, and the comparison demonstrates its practical utility.
JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION
(2023)
Article
Automation & Control Systems
Xin Liu, Xianqiang Yang, Xiaofeng Liu
Summary: This paper presents a robust identification solution for the nonlinear state-space model polluted by unknown outliers, using the heavy-tailed Laplace distribution to describe the output measurement process. By decomposing the Laplace distribution as a scale mixture of Gaussian distributions, the algorithm proves to be robust for outliers. The proposed algorithm demonstrates its usefulness and robustness through numerical examples, including a common chemical process model.
INTERNATIONAL JOURNAL OF CONTROL
(2021)
Article
Mathematics, Interdisciplinary Applications
Mustafa C. Korkmaz, Victor Leiva, Carlos Martin-Barreiro
Summary: This article introduces the properties of the continuous Bernoulli distribution and derives a quantile regression model using the exponentiated continuous Bernoulli distribution. Monte Carlo simulation studies evaluate the performance of point and interval estimators for both the continuous Bernoulli distribution and the fractile regression model. Real-world datasets from science and education are analyzed to illustrate the modeling abilities of the continuous Bernoulli distribution and the exponentiated continuous Bernoulli quantile regression model.
FRACTAL AND FRACTIONAL
(2023)
