In high-dimensional genomics studies, elastic net has gained wide popularity for its ability to accommodate structured sparsity, including multicollinearity among omics features. Recently, efforts to robustify elastic net have garnered considerable attention, as data heterogeneity in terms of outliers and heavy-tailed errors in disease phenotypes are frequently encountered. However, statistical inference procedures for robust elastic net remain underdeveloped. To fill the gap, we propose a new robust Bayesian elastic net that leads to superior performance in model fitting and especially statistical inference in the presence of heavy-tailed errors. Specifically, we have developed a fully Bayesian method that builds on a robust likelihood function to safeguard against heterogeneity of complex diseases while accounting for strong correlations. Incorporation of spike-and-slab priors in the Bayesian hierarchical model has significantly improved accuracy in shrinkage estimation, variable selection and statistical inference by inducing exact sparsity through posterior estimates generated from the Metropolis-within-Gibbs sampling. Our numeric study suggests that the new robust elastic net yields valid Bayesian credible intervals with nominal coverage probabilities even on finite samples contaminated with outliers. Furthermore, the analysis of SNP data from the Nurses' Health Study (NHS) has demonstrated the superiority of the proposed method over alternative approaches.

In the paper, we study the estimation and empirical likelihood of the parameter of interest in semiparametric varying coefficient models with right censored response data. The doubly robust and efficient estimation, along with bias-corrected empirical likelihood ratio of the regression parameter are constructed, and the estimators of the coefficient functions and the link function are also constructed. The uniformly convergence rates and asymptotic normality of the proposed estimators are presented, and the consistent estimators of the asymptotic variances are given. A more efficient estimation of the regression parameter is obtained, and the Wilks' phenomenon of the proposed ratio is proved. The obtained results can be directly used to construct confidence regions/intervals for the regression parameter and pointwise confidence intervals for the coefficient functions. The proposed method is evaluated by a simulation study and illustrated by real data analysis.

{Statistical analysis demonstrates a significant improvement in reliability studies and survival analysis based on progressively Type-II right censored samples.} This research article presents a methodology for selecting removal schemes based on progressively Type-II right censored samples. This approach addresses a significant challenge in the application of progressive Type-II right censoring and establishes an effective removal scheme applicable to various contexts in reliability studies and survival analysis. We introduce a novel approach where the nature of the experiment directly influences the removal scheme, resulting in the implementation of an informative censoring plan. To achieve this, we employ the Rayleigh-Poisson distribution for lifetime data, along with two types of distributions for random removals: the truncated Poisson distribution and the truncated discrete Rayleigh distribution. The discussion then turns to the estimation of parameters and the optimal censoring schemes. We derive the maximum likelihood estimators and compare our new approaches with removal patterns obtained from discrete binomial distributions, which are widely used in the related literature, using a Monte Carlo simulation study. This comparison evaluates biases, root mean squared errors, the covariance between estimators, and the expected total time required for the experiment. Additionally, we demonstrate the suitability of the proposed model and methodology using a real COVID-19 mortality rate dataset.

Risk difference (RD) is widely used to assess the impact of exposure in biomedical and epidemiological studies. When studying rare events, the negative binomial distribution is often preferred over the binomial distribution to ensure a sufficient number of cases of interest. This study introduces a family of new confidence interval (CI) estimators for the RD between two independent negative binomial proportions, using the method of variance estimates recovery (MOVER). These methods apply various CIs, including exact, score, fiducial, Bayesian and a modified Jeffreys interval. The modified Jeffreys approach employs a pair of proportion-specific prior parameters to derive confidence limits for the RD. The evaluation results indicate that the modified Jeffreys and fiducial methods maintain coverage probabilities closest to the nominal level while producing interval widths comparable to those of the other methods, particularly in small-sample setting. A real-data examples further illustrate the practical advantages of the proposed methods.

A new distribution-free Phase II Shewhart max-type control chart is proposed for joint monitoring of process location and scale parameters. The method combines the Van der Waerden (VW) test for location and the Mood test for scale, ensuring robustness across diverse distributions. A regression-based approximation is developed to determine control limits without extensive simulations. Monte Carlo studies evaluate the average run length (ARL) performance and compare the proposed chart with existing Shewhart-type charts, including the Shewhart max-type chart based on the Wilcoxon rank-sum (WRS) and Ansari-Bradley (AB) tests, the Shewhart-Lepage chart, the Shewhart-Cucconi chart, and the Shewhart-Lepage-type chart based on VW and Mood tests. Results show superior or competitive detection of location, scale and joint shifts across normal, lognormal, Laplace and logistic distributions, with robustness under asymmetric and heavy-tailed settings. A real data application demonstrates its effectiveness.

{A novel Bayesian approach using horseshoe priors is developed for exponential random graph models (ERGMs), addressing degeneracy and improving inference. Simulation studies demonstrate superior performance over classical ERGMs.} Exponential Random Graph Models (ERGMs) are widely used for analyzing network data but often face challenges such as parameter estimation difficulties and model degeneracy. This paper introduces the Bayesian Horseshoe Prior ERGM (BHSERGM), a hierarchical Bayesian framework that leverages the adaptive shrinkage of the horseshoe prior to improve inference in sparse, high-dimensional networks. Implemented via a parallel adaptive direction sampling algorithm, BHSERGM enhances computational efficiency and convergence. Simulation studies and empirical applications demonstrate that BHSERGM shows improved estimation accuracy and enhanced recovery of network structure compared to conventional Bayesian ERGMs, while its adaptive regularization approach appears effective in mitigating degeneracy issues commonly encountered in standard ERGM frameworks.

A fundamental challenge in comparing two survival distributions with right-censored data is the selection of an appropriate nonparametric test, as the power of standard tests like the Log-rank and Wilcoxon is highly dependent on the often-unknown nature of the alternative hypothesis. This paper introduces a new, distribution-free two-sample test designed to overcome this limitation. The proposed method is based on a strategic decomposition of the data into uncensored and censored subsets, from which a composite test statistic is constructed as the sum of two independent Wilcoxon statistics. This design allows the test to automatically and inherently adapt to various patterns of difference – including early, late, and crossing hazards – without requiring pre-specified parameters, pre-testing, or complex weighting schemes. An extensive Monte Carlo simulation study demonstrates that the proposed test robustly maintains the nominal Type I error rate. Crucially, its power is highly competitive with the optimal traditional tests in standard scenarios and superior in complex settings with crossing survival curves, while also exhibiting remarkable robustness to high levels of censoring. The test's power effectively approximates the maximum power achievable by either the Log-rank or Wilcoxon tests across a wide range of alternatives, offering a powerful, versatile, and computationally simple tool for survival analysis.

This paper investigates statistical inference for the stress–strength reliability parameter R = P ( X < Y ) and the reliability function R ( t ) , where X and Y are independent random variables following Lomax–Rayleigh distributions and data are observed as upper record values. Under the classical framework, the maximum likelihood estimator and uniformly minimum variance unbiased estimator are derived, and exact, asymptotic, and bootstrap confidence intervals are constructed. Bayesian estimation is developed under the square error loss function using both informative and non-informative priors, with inference carried out via Lindley's approximation and Markov Chain Monte Carlo methods. Simulation results demonstrate that Bayesian estimators generally provide improved estimation accuracy in terms of mean squared error, while exact and bootstrap intervals exhibit more reliable coverage performance than asymptotic intervals for moderate record sizes. The proposed procedures are illustrated with a real data application. The study extends record-based stress–strength reliability analysis to a flexible heavy-tailed lifetime model and provides a unified inferential framework applicable to reliability experiments involving extreme observations.

A probability-generating function (PGF) approach is used to derive steady-state probabilities and analyse the performance of M/M/1 queueing model, demonstrating significant improvements in the optional working vacation model and cost optimization. This paper focuses on the strategic analysis of M/M/1 queue systems with optional working vacations and customer decision-making. The proposed model introduces two types of differentiated working vacations with distinct service rates and explores customer balking and impatience during these periods. The study’s novelty lies in the integration of optional working vacation strategies, allowing dynamic adjustments based on queue conditions, which significantly enhance system efficiency and adaptability. Key performance metrics, including expected system size, waiting times and cost functions, are derived and analysed. Numerical examples illustrate the impact of various system parameters, such as arrival rates, service rates and vacation durations, on system performance and cost-efficiency. The findings provide valuable insights for designing and optimizing real-world queueing models.

Generating accurate extremes from an observational data set is crucial when seeking to estimate risks associated with the occurrence of future extremes which could be larger than those already observed. Applications range from the occurrence of natural disasters to financial crashes. Generative models from the machine learning (ML) community do not apply to extreme samples without careful adaptation. Besides, asymptotic results from extreme value theory (EVT) give a theoretical framework to model multivariate extreme events. Bridging these two fields, this paper details a variational autoencoder (VAE) approach for sampling multivariate heavy-tailed distributions, in which extremes of particularly large intensity are likely to occur. We illustrate the relevance of our approach on a synthetic data set and on a real data set of discharge measurements along the Danube river network. The latter shows the potential of our approach for flood risks' assessment. In addition to outperforming the vanilla VAE for the tested data sets, we also provide a comparison with a competing EVT-based generative approach. In the tested cases, our approach better captures the dependence structure between extreme events.