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Session-specific features of a laboratory experiment, if those exist, do not disappear by clustering standard errors at the session level. Randomly ordering or counterbalancing sessions to deal with sampling issues, cannot justify clustering the standard errors at the session level. Unlike empirical studies, for laboratory experimental studies, the experimental design reflected on the researchers' intention should primarily determine the clustering level. In a typical controlled laboratory experiment where subjects make choices in the same environment repeatedly, clustering at a participant level is intended by the experimental design, and standard errors could be larger (that is, a statistical inference could be more conservative) when clustered at the individual or decision-group level than the session level. It implies that clustering standard errors at the session level can lead to false-positive treatment effects if it is mistakenly chosen. Having a small per-session sample to increase the number of sessions could yield undesirable heterogeneities that are hard for the experimenter to control or observe.

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We study the interrelationships among concavity and weaker concavity notions of multi-variable functions, with or without differentiability. We show that modularity and homogeneity play central roles. Our characterizations offer illuminations on the nature of and the linkages among these function properties, and can be used in establishing economically meaningful results without appealing to derivatives.

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This study compares the performance of statistical models and various machine learning methods in predicting corporate bankruptcy using financial and macroeconomic data from publicly listed companies. It also analyzes the effectiveness of oversampling methods in addressing the class imbalance problem. The empirical analysis employs logistic regression, random forest, XGBoost (extreme gradient boosting), and deep neural networks, along with oversampling techniques such as SMOTE (synthetic minority over-sampling technique) and ADASYN (adaptive synthetic sampling). The results show that XGBoost delivers the most accurate and balanced predictive performance across both the original dataset and the oversampled datasets. In contrast, logistic regression exhibits high recall but limited practical applicability due to its low precision. These findings suggest that combining oversampling techniques with machine learning models such as XGBoost provides a more effective and practical approach to bankruptcy prediction in the context of imbalanced data.