A Central Limit Theorem for non-overlapping return times

Berry-Esseen type estimate and return sequence for parabolic iteration in the upper half-plane

Two different aspects of parabolic iteration in the complex upper half-plane are considered here. First, from a noncommutative probability perspective, a Berry-Esseen type estimate for the convergence speed of the monotone central limit theorem is proved. Secondly, if the underlying measure in this central limit process is singular to the Lebesgue measure on the real line, then the iteration is shown to be an infinite-measure preserving dynamical system that has a regularly varying return sequence of index 1/2.

半重尾样本协方差矩阵预解式迹的中心极限定理

Central Limit Theorem for traces of the resolvents of half-heavy tailed Sample Covariance matrices

该研究针对元素为独立同分布半重尾、维数比趋于正的样本协方差矩阵，推导其Stieltjes变换的中心极限定理并计算协方差核，还拓展得到重叠样本协方差矩阵对应Stieltjes变换的中心极限定理。

Central Limit Theorem for stationary Fleming--Viot particle systems in finite spaces

We consider the Fleming--Viot particle system associated with a continuous-time Markov chain in a finite space. Assuming irreducibility, it is known that the particle system possesses a unique stationary distribution, under which its empirical measure converges to the quasistationary distribution of the Markov chain. We complement this Law of Large Numbers with a Central Limit Theorem. Our proof essentially relies on elementary computations on the infinitesimal generator of the Fleming--Viot particle system, and involves the so-called $π$-return process in the expression of the asymptotic vari…

由时间序列构造的统计泛函的重叠批次置信区间：在分位数、优化和估计中的应用

Overlapping Batch Confidence Intervals on Statistical Functionals Constructed from Time Series: Application to Quantiles, Optimization, and Estimation

本文提出基于重叠批次与 OB-x 极限的时间序列统计泛函置信区间方法，在多种估计任务中显著优于子采样和 bootstrap。