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高维线性回归推断：基于 ℓ² 弱收敛AI 解读

We prove weak convergence in a separable Hilbert space for estimators of high-dimensional regression coefficients, which yields asymptotic normality and enables direct use of standard asymptotic tools such as the continuous mapping theorem. The approach permits diverging sparsity with many small nonzero coefficients, while requiring that only finitely many have moderate magnitude. As applications, we develop a test for finitely many linear hypotheses and, via a Scheffé-type…

利用 LU 分解识别与估计结构向量自回归模型AI 解读

Structural vector autoregressive (SVAR) models are widely used to analyze the simultaneous relationships between multiple time-dependent data. Various statistical inference methods have been studied to overcome the identification problems of SVAR models. However, most of these methods impose strong assumptions for innovation processes such as the uncorrelation of components. In this study, we relax the assumptions for innovation processes and propose an identification method…

高维随机过程模型的 Dantzig 选择器两步估计AI 解读

We consider the sparse estimation for stochastic processes with possibly infinite-dimensional nuisance parameters, by using the Dantzig selector which is a sparse estimation method similar to $Z$-estimation. When a consistent estimator for a nuisance parameter is obtained, it is possible to construct an asymptotically normal estimator for the parameter of interest under appropriate conditions. Motivated by this fact, we establish the asymptotic behavior of the Dantzig…

整数值自回归模型中计数序列的检验AI 解读

The integer autoregressive (INAR) model is one of the most commonly used models in nonnegative integer-valued time series analysis and is a counterpart to the traditional autoregressive model for continuous-valued time series. To guarantee the integer-valued nature, the binomial thinning operator or more generally the generalized Steutel and van Harn operator is used to define the INAR model. However, the distributions of the counting sequences used in the operators have…

高维平稳时间序列的稀疏主成分分析AI 解读

We consider the sparse principal component analysis for high-dimensional stationary processes. The standard principal component analysis performs poorly when the dimension of the process is large. We establish the oracle inequalities for penalized principal component estimators for the processes including heavy-tailed time series. The rate of convergence of the estimators is established. We also elucidate the theoretical rate for choosing the tuning parameter in penalized…