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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…

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…

高维回归中树引导特征聚合的直接方法AI 解读

In high-dimensional linear models, sparsity is often exploited to reduce variability and achieve parsimony. Equi-sparsity, where one assumes that predictors can be aggregated into groups sharing the same effects, is an alternative parsimonious structure that can be more suitable in certain applications. Previous work has clearly demonstrated the benefits of exploiting equi-sparsity in the presence of ``rare features'' (Yan and Bien 2021). In this work, we propose a new…

CoCoLasso：高维变量误差回归的凸方法AI 解读

Much theoretical and applied work has been devoted to high-dimensional regression with clean data. However, we often face corrupted data in many applications where missing data and measurement errors cannot be ignored. Loh and Wainwright (2012) proposed a non-convex modification of the Lasso for doing high-dimensional regression with noisy and missing data. It is generally agreed that the virtues of convexity contribute fundamentally the success and popularity of the Lasso.…

折叠凹惩罚估计的强 oracle 最优性AI 解读

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To…

混合数据的高维半参数潜在图模型AI 解读

Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete variables or a combination of both continuous and discrete variables poses new challenges in statistical modeling. In this paper, we propose a semiparametric model named latent Gaussian copula model for binary and mixed data. The observed…