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新加坡国立大学栗家量(LI JIALIANG)副教授:Semiparametric Model Averaging Prediction for Dichotomous Response

光华讲坛——社会名流与企业家论坛第 5871 期

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主题Semiparametric Model Averaging Prediction for Dichotomous Response

主讲人新加坡国立大学栗家量(LI JIALIANG)副教授

主持人统计学院林华珍教授

时间2020年10月27日(周二)上午10:30-11:30

直播平台及会议ID腾讯会议,208 544 869

主办单位:统计研究中心和统计学院 科研处

主讲人简介:

         栗家量,新加坡国立大学统计与应用概率系副教授,2001年中国科学技术大学获得统计学学士学位,分别于2005年和2006年在美国威斯康星大学麦迪逊分校获得公共健康学硕士学位和统计学博士学位。现在研究兴趣包括个性化医学、诊断医学、 预测、平滑处理、统计学习、 生存分析等。已发表论文近140篇,专著1本。他是ASA的Fellow和ISI的Elected Member。他曾为Biometrics的Associate Editor,现为BIOMARKERS的Statistics Editor,Communications for Statistical Applications and Methods、Biostatistics & Epidemiology和Lifetime Data Analysis的Associate Editor。详情请见其个人主页:https://blog.nus.edu.sg/jialiang/

内容提要:

    Model averaging has attracted abundant attentions in the past decades as it emerges as an impressive forecasting device in econometrics, social sciences and medicine. So far most developed model averaging methods focus only on either parametric models or nonparametric models with a continuous response. In this paper, we propose a semi-parametric model averaging prediction (SMAP) method for a dichotomous response. The idea is to approximate the unknown score function by a linear combination of one-dimensional marginal score functions. The weight parameters involved in the approximation are obtained by first smoothing the nonparametric marginal scores and then applying the parametric model averaging via a maximum likelihood estimation. The proposed SMAP provides greater flexibility than parametric models while being more stable than a fully nonparametric approach. Theoretical properties are investigated in two practical scenarios: (i) covariates are conditionally independent given the response; and (ii) the conditional independence assumption does not hold. In the first scenario, we show that SMAP puts weight one to the true model and hence the model averaging estimators are consistent. In the second scenario in which a “true" model may not exist, SMAP is shown to be asymptotically optimal in the sense that its Kullback-Leibler loss is asymptotically identical to that of the best but infeasible model averaging estimator. Empirical evidences from simulation studies and a real data analysis are presented to support and illustrate our methods.

    在过去的几十年中,模型平均已经成为计量经济学,社会科学和医学领域中重要的预测方法,引起了广泛的关注。到目前为止,大多数现存的模型平均方法仅关注具有连续响应的参数模型或非参数模型。本文中,我们提出了一种用于离散的二值响应变量的半参数模型平均预测(SMAP)方法。这个想法是通过一维边际得分函数的线性组合来近似未知得分函数。首先我们通过对非参数边际得分进行平滑处理,然后将最大似然估计用于参数模型平均,即可获得近似中涉及的权重参数。另外,本文所提出的SMAP比参数模型具有更大的灵活性,同时比完全非参数方法更稳定。本文在两种实际可能存在的情形下研究了相应的理论性质:(i)协变量在给定响应的条件下是独立的; ii)该条件独立性假设不成立。在第一种情况下,我们证明了SMAP相当于将权重1代入真实模型中,因此模型平均估计量是一致的。在第二种情况下,“真实”模型可能不存在,但SMAP被证明是渐近最优的,因为它的Kullback-Leibler损失与最优但不可行的模型平均估计量的KL损失渐近相同。最后,我们还进行了实际数据分析来支持和说明我们的方法。



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