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Hájek 卷积定理的二阶扩展及统计应用AI 解读

For a class of regular estimators, Hájek, in his celebrated ``Convolution Theorem,'' showed that the asymptotic distribution of a regular estimator is the convolution of the distribution of an efficient estimator and some residual distribution. This result constitutes the foundation of the concept of asymptotic efficiency of regular estimators. In this paper, we provide a second-order version of that classical result. Introducing a class of second-order regular estimators…

ANOVATS：检测海洋研究中短时间序列组间差异的子抽样检验AI 解读

Assessing marine ecosystems is important for understanding the impacts of climate change and human activity, as well as for maintaining healthy oceans and ecosystems. In marine science, it is common for biologists and geologists to identify regional differences based on expert knowledge, frequently through data visualization. However, time series data collected through surveys in marine studies typically span only a few decades, limiting the applicability of classical time…

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…

局部格兰杰因果关系的统计推断AI 解读

Granger causality has been employed to investigate causality relations between components of stationary multiple time series. We generalize this concept by developing statistical inference for local Granger causality for multivariate locally stationary processes. Our proposed local Granger causality approach captures time-evolving causality relationships in nonstationary processes. The proposed local Granger causality is well represented in the frequency domain and estimated…