🤖 AI Summary
To address low detection sensitivity and frequent omission of rare classes in heterogeneous populations, this paper proposes a covariate-dependent adaptive thresholding method. The method establishes, for the first time, a theoretical framework for the optimal adaptive threshold function, derives its asymptotic properties via nonparametric estimation, and proves a central limit theorem to support statistical inference under conditional mean and variance assumptions. It achieves precise rare-event identification through standardized statistic monitoring, proportional rule modeling, nonparametric function estimation, and bootstrap-based uncertainty quantification. Simulation and empirical studies demonstrate that, compared with conventional fixed-threshold approaches, the proposed method significantly improves alarm sensitivity while maintaining strong false-alarm control and robust inferential performance. This work provides a novel paradigm for dynamic monitoring and screening in imbalanced data settings.
📝 Abstract
Suppose (standardized) measurements or statistics are monitored to raise an alarm when a threshold is exceeded. Often, the underlying population is heterogenous with respect to important discrete variables and thus samples may consist of imbalanced classes. We propose to use thresholds which depend on such covariates to boost the sensitivity for rare classes, which otherwise tend to be ignored. Under mild conditions, we identify optimal threshold functions and develop a feasible procedure for their computation. Further, for the proportional rule a nonparametric estimator of the threshold function is proposed and a central limit theorem is shown, including the case that conditional mean and variance used for standardization are estimated. For feasible uncertainty quantification a bootstrap scheme is proposed. The approach is illustrated and evaluated by a real data analysis.