The univariate calibration problem is investigated, where different instruments, methods or laboratories are used to obtain response variables and explanatory variables in a linear regression model. We develop the objective Bayesian analysis for this problem by proposing a first and second order matching prior and a reference prior. It is shown that the posterior is improper under the second order matching prior, while the reference priors satisfy a first order matching criterion. We also provide conditions for proper posterior distributions with general priors such as matching and reference priors. The simulation study reveals that the matching prior is more effective than Jeffreys’ prior and the reference priors in terms of the target coverage probabilities in a frequentist sense, and a real example is given to illustrate the results.

The proliferation of large-scale, high-dimensional datasets characterized by inherent hierarchical structures presents significant challenges for conventional multiple testing procedures, which typically fail to leverage structural information to enhance statistical power. This paper introduces an Adaptive Multi-level Benjamini-Hochberg (AMBH) procedure specifically designed for hierarchical hypothesis testing. As an empirical presentation that complements and extends the theoretical framework developed in Bogomolov et al. (2021), our work emphasizes step-by-step implementation, evaluates the performance properties of the procedure from an empirical perspective, and provides a comparative analysis of differential performance attributes across procedures. The proposed method operates by recursively computing group-level p-values in a bottom-up manner and adaptively adjusting rejection thresholds in a top-down fashion, utilizing rejection counts from higher levels to inform thresholds determination at lower levels. This approach is particularly advantageous in settings where signals are clustered within specific branches of the hierarchy. We establish that the AMBH procedure controls both the group-level false discovery rate (GDR) at each level and a cluster-weighted false discovery rate (CWFDR). Numerical simulations demonstrate that AMBH achieves improved detection power and lower FDR compared with the conventional procedures. An application to flow cytometry data illustrates its effectiveness in detecting differential cell populations.

Simulation studies and real-data analysis are used to demonstrate the robustness and accuracy improvements of Support Vector M-Quantile Regression in nonlinear regression. This paper proposes a novel regression framework, Support Vector M-Quantile Regression (SVMQR), which integrates the robustness of M-quantile regression with the nonlinear modeling power of Support Vector Machines. Unlike traditional Support Vector Quantile Regression (SVQR), which relies on the asymmetric pinball loss, SVMQR leverages the Huber loss function to enhance resistance to outliers and improve estimation accuracy in heavy-tailed and contaminated settings. The dual formulation of the model is derived, and an efficient algorithm is implemented. Through extensive simulation studies under various error distributions and a real-world application to the Medical Cost Personal Dataset, SVMQR consistently outperforms SVQR and SVR across multiple metrics, including Pinball Loss, MAE, and RMSE. These results confirm the effectiveness of SVMQR in providing robust and accurate quantile estimates, particularly in challenging data environments characterized by heteroscedasticity and non-normality.

This study examines the relationships among risk perception, self-efficacy, and career-related anxiety among higher vocational students. Specifically, risk perception is conceptualized as students perceived uncertainty regarding employment and future career prospects. Data were collected from 300 higher vocational students enrolled in educational institutions in Guangdong Province, China, using a structured questionnaire. The data was analyzed using statistical techniques including descriptive analysis, reliability and validity testing, correlation analysis, structural equation modeling (SEM), and one-way ANOVA. The results indicate a moderate positive relationship between risk perception and self-efficacy and weak but statistically significant positive relationships between risk perception and anxiety, as well as between self-efficacy and anxiety. Structural model findings reveal that risk perception has a stronger direct effect on anxiety compared to self-efficacy, although the overall explanatory power of the model remains limited. The findings suggest that higher levels of perceived career uncertainty are associated with increased anxiety among vocational students. Contrary to conventional expectations, self-efficacy demonstrates a weak positive association with anxiety, which may reflect heightened awareness of career challenges among more confident students. These findings highlight the importance of addressing employment-related uncertainties and strengthening students’ psychological preparedness to support their mental well-being and academic development.

In this paper, we introduce an integer-valued threshold process that incorporates a random perturbation term with a negative binomial distribution, based on a generalized binomial thinning operator. We discuss the fundamental probabilistic and statistical properties of the model. The conditional least squares estimator and the conditional maximum likelihood estimator are examined for two scenarios: the threshold variable is known and unknown. Additionally, we derive the asymptotic properties of these estimators. Finally, the paper presents a numerical analysis of the estimation results as well as an example with real data.

Early detection of lung nodules, a premature form of lung cancer, and their assessment can minimize their occurrence to a great extent. Detection of white, round shadows as lung nodules in computed tomography (CT) scans is critical in determining lung cancer accurately. Despite this, challenges must still be overcome due to the lack of adequate annotated datasets, large inter-class similarities, and large intra-class variations, which make their applicability in practice very difficult. In this work, a hybrid deep learning method for lung cancer identification is proposed. The procedure starts with pre-processing of CT scan images by resizing, normalization, and format conversion. Segmentation is done by using U-Net (R-231), which automatically detects important anatomical structures. Segmented images are fed to feature extraction using GLCM and ResNet, and important features are subsequently chosen using the fossa optimization algorithm. Lastly, lung cancer detection is performed with the proposed MambaInceptXt approach, a hybrid of Inception NeXT and Mamba, showing improved detection performance. Finally, experimentation evaluation states that the proposed technique achieves enhanced results for accuracy, specificity, recall, precision, F1 score, merkel cell carcinoma (MCC), and kappa with the values of 0.965, 0.966, 0.978, 0.941, 0.959, 0.919, and 0.917.

The article proposes a step-up closed multiple testing procedure designed to evaluate the uniformity across all subsets of location parameters within k exponential distributions characterized by location and scale parameter. The proposed procedure (PP) ensures strong control of the family wise error rate. The computational approach for determining critical constants is detailed for k = 3 , while simulated critical constants are computed for specific configurations for population of size greater than 3 . A Monte Carlo simulation study evaluates the estimated power of the PP under various alternative hypothesis configurations. Additionally, a graphical comparison illustrates that the PP outperforms the existing procedures in terms of the computed estimated power. A numerical example is provided to demonstrate the practical application of the proposed method.

Classical estimators, the cornerstones of statistical inference, face insurmountable challenges when applied to important emerging classes of Archimedean copulas. These models exhibit pathological properties, including numerically unstable densities, a restrictive lower bound on Kendall’s tau, and vanishingly small likelihood gradients, making MLE brittle and limiting MoM’s applicability to datasets with sufficiently strong dependence (i.e. only when the empirical Kendall’s τ exceeds the family’s lower bound ≈ 0.545 ). We introduce IGNIS, a unified neural estimation framework that sidesteps these barriers by learning a direct, robust mapping from data-driven dependency measures to the underlying copula parameter θ . IGNIS utilizes a multi-input architecture and a theory-guided output layer ( softplus ( z ) + 1 ) to automatically enforce the domain constraint θ ̂ ≥ 1 . Trained and validated on four families (Gumbel, Joe, and the numerically challenging A1/A2), IGNIS delivers accurate and stable estimates for real-world financial and health datasets, demonstrating its necessity for reliable inference in modern, complex dependence models where traditional methods fail. To our knowledge, IGNIS is the first standalone, general-purpose neural estimator for Archimedean copulas (not a generative model or likelihood optimizer), delivering direct, constraint-aware θ ̂ and readily extensible to additional families via retraining or minor output-layer adaptations.

Statistical dependence and stochastic orders are two common tools used in distribution theory or, broadly speaking, reliability theory. In the context of the present work, we draw attention to the fact that reliability practitioners usually assume that the components constituting a system work independently. However, there are instances where the components are found to be stochastically dependent following a certain multivariate distribution. This gives rise to some error in computation of aging functions. In this paper, we propose a method based on statistical dependence and stochastic orders to compute the error incurred due to the faulty assumption that components are independently working. Our method makes the task of error analysis readily comprehensible. Earlier, the authors working in this direction considered some bivariate distributions and inferred about over/under assessment (OA/UA) of aging functions in silos, viz., survival function (SF), hazard rate, mean residual life function. However, in our work, we propose that OA/UA in the SF is closely related to statistical dependence, and OA/UA in some specific aging functions can be inferred with the help of stochastic orders, assuming that the orders for some other class of aging functions are known.

This study presents a deep learning-based technique for attack recognition in IoT networks, specifically using a hybrid model, named multi-kernel support vector attention autoencoder (MKSV-Attention Autoencoder), to detect botnet attacks. At first, traffic data is collected and then preprocessed by employing a number of steps to improve data balance and quality. Here, the missing data imputation, min–max normalization, and synthetic minority oversampling technique are exploited for preprocessing. Then, feature selection is done by using the LASSO model. Following that, attack detection in IoT is performed by utilizing the proposed MKSV-Attention Autoencoder. Finally, the experimentation evaluation is performed by employing metrics, such as accuracy, recall, precision, F1 score, TNR, and FAR. The assessment indicates that the proposed model attained a maximal accuracy of 0.9651, a precision of 0.9649, a recall of 0.9653, an F-measure of 0.9651, a TNR of 0.9649, a FAR of 0.0351, and a balanced accuracy of 0.9651.