光华讲坛——社会名流与企业家论坛第 5125 期
主 题：A spline-assisted semiparametric approach to nonparametric measurement error models
主办单位：统计研究中心 统计学院 科研处
马彦源，现为宾夕法利亚州立大学教授，是麻省理工学院应用数学博士，北京大学数学学士。其研究兴趣包括：Semiparametrics，Measurement error models，Mixed sample problems，Latent variable models，Dimension reduction，Selection bias and Skew-elliptical distributions。主持科研项目9项，已公开发表论文100余篇。特邀报告约190场。
Nonparametric estimation of the probability density function of a random variable measured with error is considered to be a difficult problem, in the sense that depending on the measurement error property, the estimation rate can be as slow as the logarithm of the sample size. Likewise, nonparametric estimation of the regression function with errors in the covariate suffers the same possibly slow rate. The traditional methods for both problems are based on deconvolution, where the slow convergence rate is caused by the quick convergence to zero of the Fourier transform of the measurement error density, which, unfortunately, appears in the denominators during the construction of these methods. Using a completely different approach of spline assisted semiparametric methods, we are able to construct nonparametric estimators of both density functions and regression mean functions that achieve the same nonparametric convergence rate as in the error free case. Other than requiring the error-prone variable distribution to be compactly supported, our assumptions are not stronger than in the classical deconvolution literatures. The performance of these methods are demonstrated through some simulations and a data example.