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尖峰协方差结构下高维无岭最小二乘插值的预测风险AI 解读

This paper investigates the asymptotic behavior of the out-of-sample prediction risk of the high-dimensional ridgeless least-squares estimator when the feature dimension $p$ and the sample size $n$ grow proportionally. We consider a generalized spiked population covariance model with multiple latent factors, where the number of spiked eigenvalues may remain finite or increase with $n$, and the spiked eigenvalues may be bounded or diverge at arbitrary rates. Beyond…

异质环境下的不变量分位数回归AI 解读

In this paper, we propose an invariant quantile regression (IQR) framework specifically designed for multi-environment datasets, which captures the invariance across different environments. This framework is closely related to transfer learning, causal inference, and fair machine learning, and is motivated by scenarios in which the conditional probability of the response given covariates varies, while certain key variables remain invariant. This perspective differs notably…

高维因子增强稀疏线性模型的迁移学习AI 解读

In this paper, we study transfer learning for high-dimensional factor-augmented sparse linear models, motivated by applications in economics and finance where strongly correlated predictors and latent factor structures pose major challenges for reliable estimation. Our framework simultaneously mitigates the impact of high correlation and removes the additional contributions of latent factors, thereby reducing potential model misspecification in conventional linear modeling.…

大维广义因子模型中的因子个数确定AI 解读

This paper proposes new estimators of the number of factors for a generalised factor model with more relaxed assumptions than the strict factor model. Under the framework of large cross-sections $N$ and large time dimensions $T$, we first derive the bias-corrected estimator $\hat σ^2_*$ of the noise variance in a generalised factor model by random matrix theory. Then we construct three information criteria based on $\hat σ^2_*$, further propose the consistent estimators of…