团队

前不久，2026年8月2日，欧盟《人工智慧法》核心条款正式生效：所有AI生成内容必须清晰标注，聊天机器人必须告知用户正在与AI互动，违规企业最高面临1500万欧元或全球年营业额3%的罚款。这不是一份可以选择遵守的行业倡议，而是具有法律约束力的监管底线——AI信任，已经从企业内部的道德自觉，变成外部强制的合规要求。

Traditional functional linear regression usually takes a one-dimensional functional predictor as input and estimates the continuous coefficient function. Modern applications often generate two-dimensional covariates, which become matrices when observed at grid points. To avoid the inefficiency of the classical method involving estimation of a two-dimensional coefficient function, we propose a functional bilinear regression model, and introduce an innovative three-term penalty to impose roughness penalty in the estimation. The proposed estimator exhibits minimax optimal property for prediction under the framework of reproducing kernel Hilbert space. An iterative generalized cross-validation approach is developed to choose tuning parameters, which significantly improves the computational efficiency over the traditional cross-validation approach. The statistical and computational advantages of the proposed method over existing methods are further demonstrated via simulated experiments, the Canadian weather data, and a biochemical long-range infrared light detection and ranging data. ©2025 Dan Yang, Jianlong Shao, Haipeng Shen, Hongtu Zhu.

Estimation of the covariance matrix of asset returns is crucial to portfolio construction. As suggested by economic theories, the correlation structure among assets differs between emerging markets and developed countries. It is therefore imperative to make rigorous statistical inference on correlation matrix equality between the two groups of countries. However, if the traditional vector-valued approach is undertaken, such inference is either infeasible due to limited number of countries comparing to the relatively abundant assets, or invalid due to the violations of temporal independence assumption. This highlights the necessity of treating the observations as matrix-valued rather than vector-valued. With matrix-valued observations, our problem of interest can be formulated as statistical inference on covariance structures under sub-Gaussian distributions, i.e., testing non-correlation and correlation equality, as well as the corresponding support estimations. We develop procedures that are asymptotically optimal under some regularity conditions. Simulation results demonstrate the computational and statistical advantages of our procedures over certain existing state-of-the-art methods for both normal and non-normal distributions. Application of our procedures to stock market data reveals interesting patterns and validates several economic propositions via rigorous statistical testing.