論文

We investigate sparse and low-rank estimation methods for the intensity functions of multivariate Hawkes processes. While univariate Hawkes processes are approximated by integer-valued autoregressive models in the weak topology, we extend this approximation result to the multivariate setting. Building on this foundation, we develop new sparse and higher-order reduced-rank estimation procedures for multivariate Hawkes processes by leveraging methodology for multivariate integer-valued time series. In addition, we study a sparse weighted least squares estimator and establish error bounds for all proposed estimators. All theoretical results are derived by verifying novel moment and mixing conditions that ensure the applicability of concentration inequalities to weakly dependent data. Finally, we conduct an empirical study to assess the finite-sample performance of all estimation methods.

This paper addressed a critical issue of reporting delays in estimating the effective reproduction number, focusing on the context of the COVID-19 pandemic. The reporting delay problem is a pervasive challenge, impacting the accuracy of the estimation and consequently influencing public health decision-making. Through the exploration of the application of the Chain Ladder method, a well-established technique from actuarial science, a novel approach to mitigate the effects of reporting delays in infectious disease epidemiology was proposed. By applying the Chain Ladder method to infectious disease data, we illustrated its potential to provide more accurate and timely estimation, accounting for reporting delays inherent in epidemiological surveillance systems.

We discuss an application of Generalized Random Forests (GRF) proposed to quantile regression for time series data. We extended the theoretical results of the GRF consistency for i.i.d. data to time series data. In particular, in the main theorem, based only on the general assumptions for time series data and trees, we show that the tsQRF (time series Quantile Regression Forest) estimator is consistent. Compare with existing article, different ideas are used throughout the theoretical proof. In addition, a simulation and real data analysis were conducted. In the simulation, the accuracy of the conditional quantile estimation was evaluated under time series models. In the real data using the Nikkei Stock Average, our estimator is demonstrated to capture volatility more efficiently, thus preventing underestimation of uncertainty.

© 2018 The Authors In this study, we develop a higher-order asymptotic theory of shrinkage estimation for general statistical models, which includes dependent processes, multivariate models, and regression models (i.e., non-independent and identically distributed models). We introduce a shrinkage estimator of the maximum likelihood estimator (MLE) and compare it with the standard MLE by using the third-order mean squared error. A sufficient condition for the shrinkage estimator to improve the MLE is given in a general setting. Our model is described as a curved statistical model p(⋅;θ(u)), where θ is a parameter of the larger model and u is a parameter of interest with dimu