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异方差下稠密高维 Huber 回归的精确渐近理论AI 解读

We study Huber regression in a heteroscedastic linear model in the proportional regime $n/p \to δ\in (1, \infty)$. Our main result is an exact characterization of the asymptotic empirical distribution of the Huber estimator. This characterization is in terms of three scalar parameters which determine the first-order centre and the asymptotic variance of the Huber estimator. The result shows that with heteroscedastic noise, the first-order centre may contain an additional…

TabCF：利用表格基础模型进行分布控制函数估计AI 解读

Instrumental variable (IV) and control function (CF) methods are powerful tools for causal effect estimation in the presence of unmeasured confounding, yet most existing approaches target only mean effects and/or demand substantial fitting and tuning effort. In this paper, we introduce a simple method, TabCF, for control function regression using tabular foundation models, which enables accurate, fast, identification-transparent, and tuning-light causal estimation of…

交叉拟合协方差校准下惩罚估计方程的假设检验AI 解读

We study hypothesis testing for penalized estimators in settings where the full marginal distribution of a multivariate response is difficult to specify, such as longitudinal data with correlated measurements or high-dimensional heteroscedastic regression. Assuming that the conditional mean model is correctly specified, we establish that the penalized estimating equations admit a $\sqrt{n}$-consistent solution, even when the working covariance structure is misspecified. Our…

基于近似消息传递的高维新纽伊-鲍威尔检验AI 解读

We propose a high-dimensional extension of the heteroscedasticity test proposed in Newey and Powell (1987). Our test is based on expectile regression in the proportional asymptotic regime where n/p \to δ\in (0,1]. The asymptotic analysis of the test statistic uses the Approximate Message Passing (AMP) algorithm, from which we obtain the limiting distribution of the test and establish its asymptotic power. The numerical performance of the test is validated through an…