題目:Dynamic Covariance Models
時間:2015年6月9日(周二)15:30-16:00
地點:6號樓415教室
主講人:諶自奇博士
主辦單位:數(shù)學與統(tǒng)計學院
Abstract:
An important problem in contemporary statistics is to understand the relations among p variables,usually with p much larger than the sample sizen. Recent efforts have been focusing on modeling static covariance matrices where pairwise covariances areconsidered invariant. In many real systems, however, these pairwise relations often change. To characterize the changing correlations in a high dimensional system, we study a class of dynamic covariance models (DCMs) assumed to be sparse, and investigate for the first time a unified theory for understanding their non-asymptotic error rates and model selection properties. In particular, in the challenging high dimension regime, we highlight a new uniform consistency theory in which the sample size can be seen as $n^{4/5}$ when the bandwidth parameter is chosen as for accounting for the dynamics, and this result holds uniformly over a range of the variable used for modeling the dynamics. The convergence rate bears the mark of the familiar bias-variance trade-off in the kernel smoothing literature. We illustrate the results with simulations and the analysis of a neuroimaging dataset.
主講人簡介
教育背景
2006.9-2012.6,東北師范大學數(shù)學與統(tǒng)計學院,概率論與數(shù)理統(tǒng)計專業(yè),碩博連讀。
2002.9-2006.6,湖南師范大學數(shù)學與計算機科學學院,數(shù)學與應用數(shù)學專業(yè),本科階段的學習。
學術(shù)服務
Referee for Statistica Sinica;Comput.Statist. Data Anal.
研究興趣
縱向數(shù)據(jù)分析,剖面似然研究,高維數(shù)據(jù)充分降維。
項目資助
國家自然科學基金青年基金,11401593,基于剖面似然的統(tǒng)計推斷,22萬元,在研,主持。
教育部高等學校博士點基金,20130162120086,高維協(xié)方差矩陣的非參數(shù)模型及其基于閾值規(guī)則的估計,4萬元,在研,主持。
第七批中國博士后科學基金特別資助,2014T70778,高維動態(tài)圖模型研究,15萬元,在研,主持。
第53批中國博士后科學基金,高維稀疏非參數(shù)協(xié)方差矩陣估計及其應用,2013M531796,5萬元,在研,主持。
國家自然科學基金青年基金,11301245,有序約束下動態(tài)處理效應的統(tǒng)計方法研究,22萬元,在研,第一合作者。
國家自然科學基金面上項目,關(guān)于有序數(shù)據(jù)的統(tǒng)計推斷,26萬元,已結(jié)題,參加。
高等院校博士生創(chuàng)新基金,縱向數(shù)據(jù)中半?yún)?shù)模型的有效估計方法與應用,09SSXT116,2萬元,已結(jié)項,主持。