Interest in continuous-time processes has increased rapidly in recent years, largely because of high-frequency data available in many applications. We develop a method for estimating the kernel function $g$ of a second-order stationary Lévy-driven continuous-time moving average (CMA) process $Y$ based on observations of the discrete-time process $Y^Δ$ obtained by sampling $Y$ at $Δ, 2Δ,...,nΔ$ for small $Δ$. We approximate $g$ by $g^Δ$ based on the Wold representation and prove its pointwise convergence to $g$ as $Δ\rightarrow 0$ for $\CARMA(p,q)$ processes. Two non-parametric estimators of $g^Δ$, based on the innovations algorithm and the Durbin-Levinson algorithm, are proposed to estimate $g$. For a Gaussian CARMA process we give conditions on the sample size $n$ and the grid-spacing $Δ(n)$ under which the innovations estimator is consistent and asymptotically normal as $n\rightarrow\infty$. The estimators can be calculated from sampled observations of {\it any} CMA process and simulations suggest that they perform well even outside the class of CARMA processes. We illustrate their performance for simulated data and apply them to the Brookhaven turbulent wind speed data. Finally we extend results of \citet{bfk:2011:1} for sampled CARMA processes to a much wider class of CMA processes.
Optimal Sampling for Kernel Quadrature on Unbounded Domains
CEREMADE, Université Paris-Dauphine, Université PSL, CNRS（CEREMADE，巴黎第九大学，巴黎文理研究大学，法国国家科学研究中心）；Department of Statistics, University of Warwick（华威大学统计系）；Université Paris-Saclay, INRAE, AgroParisTech, UMR MIA Paris-Saclay（巴黎萨克雷大学，法国国家农业食品与环境研究院，巴黎农学院，MIA巴黎萨克雷联合研究单位）
本文研究了随机 quadrature 方法，旨在提高鲁棒性而非特定核的最优性。提出了一种显式且依赖于 n 的采样分布，能够在不需了解核的情况下实现最小最大误差率，扩展到无界域，提供理论保证和实用的鲁棒最优随机 quadrature 方法。
Approximate Shapley value estimation using sampling without replacement and variance estimation via the new Symmetric bootstrap and the Doubled half bootstrap
Estimating with kernel smoothers the mean of functional data in a finite population setting. A note on variance estimation in presence of partially observed trajectories
Gain with no Pain: Efficient Kernel-PCA by Nyström Sampling
Pennsylvania State University（宾夕法尼亚州立大学）；Massachusetts Institute of Technology（麻省理工学院）；Istituto Italiano di Tecnologia（意大利技术研究院）；Universita’ degli Studi di Genova（热那亚大学）；INRIA（法国国家信息与自动化研究所）；École-Normale Supérieure, PSL Research University（巴黎文理研究大学巴黎高等师范学院）
