The generative adversarial network (GAN) is an important model developed for high-dimensional distribution learning in recent years. However, there is a need for a comprehensive understanding of its generalization error and convergence behavior. In this research, we study the generalization error of GANs based on classes of functions encompassing discriminator and generator neural networks with piecewise linear activation functions. Under our assumptions, the resulting function classes are VC type with bounded envelope functions, enabling the application of Talagrand’s inequality. By employing Talagrand’s inequality and the Borel–Cantelli lemma, we establish almost sure convergence rates for the generalization error of GANs under fixed discriminator and generator architectures. We further apply the same empirical-process technique to several existing GAN error formulations and obtain corresponding almost sure convergence bounds. The resulting sample-size dependence is compared with existing results under the same fixed-architecture setting, while network-complexity quantities are treated consistently as fixed constants with respect to the sample sizes. In particular, under suitable range and symmetry conditions on the discriminator class, the error defined by the neural network distance is a special case of our general measuring-function objective.
In reliability and actuarial studies, assessing the similarity between the probability distributions of residual or past lifetimes of two populations is a fundamental concern. Matusita’s measure is a widely used similarity metric that quantifies the degree of overlap between such distributions. This paper focuses on the nonparametric estimation of Matusita’s measure when data from both populations represent residual or past lifetimes. We propose nonparametric estimators for residual and past Matusita’s measures and study their asymptotic properties, such as consistency and asymptotic normality. Finally, we conduct a simulation study to evaluate the performance of the proposed estimators, and we apply our methodology to a real dataset to illustrate its practical utility.
The framework of stochastic frontier analysis resembles standard mixed-effect models, with the distinction of featuring errors with negative asymmetry arising from a Gaussian component that captures heterogeneity and a negatively skewed inefficiency component. Conventional maximum likelihood estimation degenerates under three persistent challenges in cross-sectional settings: finite-sample inefficiency, identifiability collapse under wrong skewness, and large-sample dependency. To overcome these limitations, a conditional parameter estimator is introduced. The estimator is consistent, asymptotically efficient, and yields closed-form score and information expressions, circumventing the computationally intensive numerical integration and nonparametric density estimation required by existing methods. Simulations establish the estimator’s superior finite-sample performance, demonstrating near-zero bias and minimal MSE across all conditions including distributional misspecification and contaminated data, while maintaining efficiency in small samples. An application to firm efficiency data demonstrates its empirical applicability, producing estimates with greater precision and stability than established methods. The estimator thus provides a robust, computationally efficient alternative for efficiency analysis, particularly in data-limited domains.
This paper introduces a new two-parameter distribution for modelling unit interval data. It is named the Unit Power-Logistic Quadratic Lindley (UPLQL) model. It is constructed by applying a power-logistic transformation to a flexible baseline distribution known as the quadratic Lindley. The resulting density can take several shapes; decreasing, unimodal, right skewed, or left skewed making it suitable for a wide variety of proportional data. Closed-form expressions for the cumulative distribution function (CDF), probability density function (PDF), and hazard rate function are formulated, while the quantile function (QF) is derived in a semi-closed-form. Mathematical properties including moments, Lorenz and Bonferroni curves, order statistics, stress-strength reliability, and stochastic order are derived. Eight frequentist estimation methods are compared through an extensive Monte Carlo simulation (MCS), and a Bayesian analysis using Markov chain Monte Carlo (MCMC) is also carried out. An amortised tree-based estimator (ATE) that predicts the parameters directly from a set of features is developed. It can be turned into a fast Bayesian tool using a parametric bootstrap. The performance of the UPLQL model is evaluated on two data sets, the flood-level proportions and petroleum reservoir measurements. In both applications, the new distribution performs competitively with established unit distributions and offers a good combination of flexibility, interpretability, and computational efficiency.
Accurate prediction of breast cancer survival is crucial for precision oncology and individualized treatment planning. Standard survival models, however, typically fail to capture nonlinear clinical relationships, latent biological heterogeneity, and complex interactions among prognostic factors. To address these limitations, this study introduces a Hybrid Machine Learning Framework that combines adaptive covariate transformation, simulated gene expression generation, cross-modal attention fusion, graph-based patient learning, dynamic multi-expert survival modeling, and Bayesian uncertainty estimation. The framework translates clinical variables into clinically meaningful latent representations of prognosis and creates biologically plausible molecular features to boost prognosis prediction. Experimental results show that the proposed model achieves better C-index, AUC, Precision, Recall, and F1-score (0.927, 0.944, 0.931, 0.924, and 0.927, respectively) and a minimum Integrated Brier Score (0.081). Survival stratification analysis clearly differentiates among the low-, intermediate-, and high-risk patient groups, and ablation analysis results support the contribution of each component of the framework. The results suggest that combining transformed clinical data with synthetic genomic data yields a powerful, interpretable, and uncertainty-aware prediction tool for breast cancer survival, with promising potential for precision oncology applications.
