A Lepskiĭ-type stopping rule for the covariance estimation of multi-dimensional Lévy processes

The Bayes Lepski's Method and Credible Bands through Volume of Tubular Neighborhoods

For a general class of priors based on random series basis expansion, we develop the Bayes Lepski's method to estimate unknown regression function. In this approach, the series truncation point is determined based on a stopping rule that balances the posterior mean bias and the posterior standard deviation. Equipped with this mechanism, we present a method to construct adaptive Bayesian credible bands, where this statistical task is reformulated into a problem in geometry, and the band's radius is computed based on finding the volume of certain tubular neighborhood embedded on a unit sphere. W…

Adaptive estimation of linear functionals in functional linear models

We consider the estimation of the value of a linear functional of the slope parameter in functional linear regression, where scalar responses are modeled in dependence of random functions. In Johannes and Schenk [2010] it has been shown that a plug-in estimator based on dimension reduction and additional thresholding can attain minimax optimal rates of convergence up to a constant. However, this estimation procedure requires an optimal choice of a tuning parameter with regard to certain characteristics of the slope function and the covariance operator associated with the functional regressor. …

Adaptive functional linear regression

We consider the estimation of the slope function in functional linear regression, where scalar responses are modeled in dependence of random functions. Cardot and Johannes [J. Multivariate Anal. 101 (2010) 395-408] have shown that a thresholded projection estimator can attain up to a constant minimax-rates of convergence in a general framework which allows us to cover the prediction problem with respect to the mean squared prediction error as well as the estimation of the slope function and its derivatives. This estimation procedure, however, requires an optimal choice of a tuning parameter wi…

一种针对顺序到达高维数据的三阶段PCA程序

A Three-Stage PCA Procedure for Sequentially Arriving High-Dimensional Data

提出一种三阶段自适应PCA程序，平衡压缩损失与采样成本，通过中间阶段更新避免依赖未知特征值，实现一阶和二阶效率，并在模拟和癌症基因数据中验证其性能。

核岭回归的自适应参数选择

Adaptive Parameter Selection for Kernel Ridge Regression

针对核岭回归的参数选择难题，本文利用其谱性质和Lepskii型原则提出早停式自适应策略，并在学习理论框架下证明其可达到最优学习率且适应不同范数。

Central limit theorems for pre-averaging covariance estimators under endogenous sampling times

We consider two continuous Itô semimartingales observed with noise and sampled at stopping times in a nonsynchronous manner. In this article we establish a central limit theorem for the pre-averaged Hayashi-Yoshida estimator of their integrated covariance in a general endogenous time setting. In particular, we show that the time endogeneity has no impact on the asymptotic distribution of the pre-averaged Hayashi-Yoshida estimator, which contrasts the case for the realized volatility in a pure diffusion setting. We also establish a central limit theorem for the modulated realized covariance, wh…