Statistical Methods in Business Analytics

We consider two systems of firms that may default, both exposed to a common systematic risk factor in addition to their respective system-specific common shock factor. While much of the existing literature focuses on a single system, we investigate joint risk due to defaults across two interdependent systems, allowing for varying dominance among the risk factors. Specifically, we explore three scenarios: (1) both systems are driven primarily by the shared systematic risk factor, (2) each system is dominated by its own common shock factor, and (3) a scenario where all three factors – the systematic risk and the two common shocks – are asymptotically dependent and jointly contribute to defaults. For each scenario, we analyze the conditional probability of large default losses in one system given large default losses in the other, which serves as a measure of contagion between the systems. The analysis is conducted under the limiting regime where individual default probabilities tend to zero. For all three scenarios, we derive asymptotic equivalences showing that the conditional probability remains strictly positive even as individual default probabilities vanish. Sensitivity analysis highlights that when systematic risk dominates, its heavy-tailedness drives the conditional probability, whereas when common shocks dominance, or when all factors joint dominate, the dependence among risk factors becomes the determining force. 

This expository paper introduces a simplified approach to image-based quality inspection in manufacturing using OpenAI's CLIP (Contrastive Language-Image Pretraining) model adapted for few-shot learning. While CLIP has demonstrated impressive capabilities in general computer vision tasks, its direct application to manufacturing inspection presents challenges due to the domain gap between its training data and industrial applications. We evaluate CLIP's effectiveness through five case studies: metallic pan surface inspection, 3D printing extrusion profile analysis, stochastic textured surface evaluation, automotive assembly inspection, and microstructure image classification. Our results show that CLIP can achieve high classification accuracy with relatively small learning sets (50-100 examples per class) for single-component and texture-based applications. However, the performance degrades with complex multi-component scenes. We provide a practical implementation framework that enables quality engineers to quickly assess CLIP's suitability for their specific applications before pursuing more complex solutions. This work establishes CLIP-based few-shot learning as an effective baseline approach that balances implementation simplicity with robust performance, demonstrated in several manufacturing quality control applications. 

Machine learning techniques have been used in a variatey of different contexts such as engineering, healthcare, and business. In this work, we propose a Multi-Task learning framework incorporating expert opinions through a novel penalty that utilizes fitted values. We also investigate other machine learning frameworks where expertise can be integrated. Insights on computational efficiency and model selection are also provided. Finally, we present. a use case for our approach in the context of maintaining health care capacity in dynamic settings. 

This paper considers an important finance problem, equity premium prediction, for which the mean regression as the standard approach can be problematic due to heteroscedasticity and heavy-tails of the error. We propose using penalized quantile regression to provide estimates of quantiles for equity premium. Many penalized quantile methods allow for the set of active variables to vary by quantile. We find increases the chances of causes crossing quantiles in the predictions. To mitigate this issue we propose using a group lasso to guarantee that the set of active variables is the same across all quantiles.