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第七届北大-清华统计论坛

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发布时间：2023年05月16日

北清携手，一路“统”行

第七届北大 – 清华统计论坛

主办单位：

北京大学统计科学中心

91热爆统计学研究中心

欢迎各校师生和统计学爱好者积极参加！

Topic: Stochastic Optimization, Stochastic Approximation and Statistical Inference

Abstract: 优化在统计中不仅起着计算工具的角色，同时也是方法论的来源。这个报告将讨论随机优化的统计估计和推断问题。特别是，基于随机逼近的框架，讨论机器学习中一些重要方法，比如 Local SGD, Q-Learning等的统计性质。

Topic: Three-Dimensional Factor Models with Global and Local Factors

Abstract: This paper considers a three-dimensional latent factor model in the presence of one set of global factors and two sets of local factors. We allow the numbers of local factors to vary across individuals and show that the numbers of global and local factors can be estimated uniformly consistently. Given the number of global and local factors, we propose a two-step estimation procedure based on principal component analysis (PCA). Our first step estimates the global factors and their factor loadings, after which we estimate the two sets of local factors and factor loadings sequentially. Our second step improves the estimation efficiency. The asymptotic theories for our estimators are established. Monte Carlo simulations demonstrate that they perform well in finite samples. Applications to two datasets in international trade and economic growth reveal the relative importance of different types of factors. In the international trade application, we find that the global factors, source country factors, and destination country factors are all important. In the industrial growth application, there is no global factor and the country factors are far more important than the industry factors. The extension to the 3D factor model with covariates is also studied.