報告題目：Conditional Test for Ultrahigh Dimensional Linear Regression Coefficients
報 告 人：崔恒建 教授 首都師範大學
報告時間：2020年7月19日 14:00-15:00
報告地點：騰訊會議ID：508 126 844
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校内聯系人：程建華 chengjh@jlu.edu.cn
報告摘要：
In this talk, we concern with a conditional test for regression coefficients in ultrahigh dimensional linear models. Conditioning on a subset of important predictors in the model, we test the overall significance of regression coefficients of the remaining ultrahigh dimensional predictors. We first propose a conditional U-statistic test (CUT) based on an estimated U-statistic for a high dimensional linear regression model and prove that its null asymptotic distribution is normal under some mild assumptions. However, the empirical power of the proposed test is inversely affected by the dimensionality of predictors. To this end, we further propose a two-stage CUT with screening (CUTS) procedure to reduce the dimensionality under the sparsity assumption and enhance the empirical power based on random data splitting strategy. In the first stage, we divide data randomly into two equal halves and apply the conditional sure independence screening to the first half to reduce the dimensionality; In the second stage, we apply the proposed CUT test to the second half. To eliminate the effect of random data splitting and further enhance the empirical power, we also develop a powerful ensemble algorithm based on multiple splitting strategy and prove that the family-wise error rate is asymptotically controlled at a given significance level. We demonstrate the excellent finite-sample performances of the proposed conditional test via Monte Carlo simulations and a real data analysis.
報告人簡介：
崔恒建，首都師範大學教授，博士生導師，曾任國務院學位委員會學科評議組專家。研究方向主要包括數理統計和穩健統計理論及方法、金融統計、遙感統計與質量管理等，在JASA、AoS、JRSSB、Biometrika和JoE等期刊上發表論文120餘篇。先後主持國家自然科學基金傑青(B)項目和4項國家自然科學基金面上項目以及青年基金項目；主要參加了國家自然科學基金重點項目、主任基金、教育部重大科研基金、科技部863計劃等科研項目15餘項。現擔任《應用數學學報》中英文版編委、《數理統計與管理》編委、中國概率統計學會常務理事、中國現場統計學會副理事長、全國工業統計教學研究會副會長、北京應用統計學會會長、生存分析分會副理事長、國際泛華統計協會會員、美國數學會數學評論員與國際數理統計學會(中國分會)常務理事。曾獲教育部高等學校科學技術獎(自然科學獎)二等獎、全國統計科學研究優秀成果獎一等獎、全國統計科學研究優秀教學成果獎二等獎、中國科協期刊優秀學術論文三等獎、北京師範大學優秀科研成果獎、國家統計局全國統計科學技術進步二等獎以及京津五四青年概率統計學術年會“蓋洛普”獎等。
