Thesis is devoted to the application of cumulant analysis in the estimation of impulse response functions for continuous time-invariant linear systems, including systems with inner noises. The main assumption of the work is the second-order integration of the impulse response function. Our study deals with cumulant analysis of sample cross-correlograms between stationary Gaussian stochastic processes. An important role was played by integral representations for the higher-order cumulants of these second-order statistics. Using the diagram formula, all representations are reduced to the finite sums of integrals involving cyclic products of kernels. In the work we proved the convergence to zero of the corresponding integrals. Then, since the Gaussian distribution is uniquelly determined by its cumulants and also all higher-order cumulants of the estimators tend to zero, we establish the asymptotic normality of the integral-type cross-correlogram estimators.
From Information Geometry to Jet Substructure: A Triality of Cumulant Tensors, Energy Correlators, and Hypergraphs
Institute of Experimental Particle Physics, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院实验粒子物理研究所）；Institute for Theoretical Physics, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院理论物理研究所）；Blackett Laboratory, Imperial College of Science, Technology and Medicine（帝国理工学院布莱克特实验室）；Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院量子材料与技术研究所）
kNN estimation in semi-functional partial linear regression with missing responses at random
Universidade da Coruña（拉科鲁尼亚大学）；Centro de Investigación en Tecnologías de la Información y las Comunicaciones (CITIC)（信息与通信技术研究中心）；Universidad Carlos III de Madrid（马德里卡洛斯三世大学）
Unifying AMP Algorithms for Rotationally-Invariant Models
Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院计算数学与科学工程计算研究所）
