时间：2016年12月12日（星期一）13:30

地点：学院南路校区图配楼514

点评：马平，马景义，孙志猛

报告人：孙枭枭，佐治亚大学统计系博士研究生

题目： Optimal Penalized Function-on-Function Regression under a Reproducing Kernel Hilbert Space Framework

摘要：Many scientific studies collect data where the response and predictor variables are both functions of time, location, or some other covariate. Understanding the relationship between these functional variables is a common goal in these studies. Motivated from two real-life examples, we propose a new function-on-function regression model that can be used to analyze such kind of functional data. Our estimator of the 2D coefficient function is the optimizer of a form of penalized least squares where the penalty enforces certain level of smoothness on the estimator. Our first result is the Representer theorem which states that the exact optimizer of the penalized least squares actually resides in a data-adaptive finite dimensional subspace although the optimization problem is defined on a function space of infinite dimensions. This theorem then allows us an easy incorporation of the Gaussian quadrature into the optimization of the penalized least squares, which can be carried out through standard numerical procedures. We also show that our estimator achieves the minimax convergence rate in mean prediction under the framework of function-on-function regression. Extensive simulation studies demonstrate the numerical advantages of our method over the existing ones. The proposed method is then applied to our motivating examples of the benchmark Canadian weather data and a histone regulation study.

报告人：刘怡文，佐治亚大学统计系博士研究生

题目：Weighted Leverage Score for Model-free Statistical Learning

摘要：In the past few decades, high dimensional data has occurred in areas such as genomics, tumor classification, image processing and Internet search. How to extract useful information from such data becomes the key issue nowadays. In high dimensional data, the“large p, small n”problem has posed many challenges to statistical analysis. Despite the urgent need in statistical tools to deal with such data, there are limited methods that can fully address the high dimensional problem. Motivated by sliced inverse regression and leverage score, we propose a novel feature screening method named weighted leverage score (WLS) under the framework of sufficient dimension reduction. Unlike linear stepwise regression, WLS screening procedure does not impose a specific form of relationship between the response variable and the predictors, and it can identify all relevant predictors consistently as demonstrated in our theoretical analysis. The WLS not only possesses consistency in selection, but also has competitive performance in empirical studies. We also applied the proposed method to a breast cancer data generated by spatial transcriptomics, and identified a group of marker genes of cancer stages.

报告人：张辛连，佐治亚大学统计系博士研究生

题目：Integrating Model Uncertainty in Statistical Inference: A Bayesian Approach

摘要:In practice, when faced with multiple candidate models, the popular approach nowadays is to perform model selection using criteria such as AIC, BIC, MSE, and march on to make the statistical inference solely based on the selected model as if it were the true model, i.e. the uncertainty in previous model selection step is not reflected, thus it is possible that false discovery might be made based on the "over-confident" statistical inference.In this project, I take a bayesian point of view and propose a mixture prior to take into account the model selection uncertainty so that it will be reflected in final statistical inference. Non informative prior and adapted Gibbs sampler for the model proposed will be developed. I will illustrate the proposed model with combination between using cubic spline and thin plate spline when applying the smoothing spline methods to a two-dimensional data.

报告人：方彤，中央财经大学统计与数学学院博士研究生；单璐琪，中央财经大学统计与数学学院硕士研究生

题目：增强型指数追踪模型设计及模型路径算法

摘要：在考虑追踪误差和超额收益基础上，本文构建同时考虑追踪误差和绝对收益的增强型指数追踪模型，通过引入广义等角度向量，提出一种新的求解增强型指数追踪问题的算法。数据模拟显示，新算法具有良好的求解能力和计算效率，与增强型指数模型求解问题具有契合性。通过数据模拟，以及与国外的5组世界主要股票市场指数及其成份股的历史数据对模型及算法进行测算，并与国外作者模型同类模型进行对比，结果表明算法相对传统预设参数算法具有良好的求解能力和计算速度。并通过追踪上证50指数进行实证分析，构建样本外预测、资产组合稀疏性、夏普比率和最大回撤进行模型效果评价，现通过限制模型中的股票个数，可以得到若干稀疏且稳定的资产组合模型。增强型指数追踪模型在国内具有较强适用性，在保证资产稀疏性的前提下得到超额收益，提高了投资组合决策过程的客观性和科学性。本文对基金公司、机构和个人投资者具有实际意义。

报告人：宋鹏，中央财经大学统计与数学学院博士研究生

题目：Modeling High-dimensional Realized Covariance Matrix via Combination of VAR Model and Regularized Variable Selection Method

摘要：Large covariance matrix estimations have become fundamental problems in multivariate analysis, which could find applications in financial econometrics field. We consider Regularized estimators to reduce the dimensionality and next investigate the sources of these driving dynamics as well as the performance of the portfolio constructed with forecasted the realized covariance matrices by proposed model.