3421ea2fc7182410VgnVCM100000c2b1d38dRCRDapproved/UMICH/stats/Home/News & Events/Statistics SeminarDepartment Seminar Series: Guang Chen, Ph.D., A Long March Towards Joint Asymptotics: My 1st Steps...###@###(Fri, 6 Dec 2013)Department Seminar Series: Guang Chen, Ph.D., A Long March Towards Joint Asymptotics: My 1st Steps...###@###(Fri, 6 Dec 2013)340 West Hallstats1386347400000138634740000011:30AM<p style=" margin-top: 0in; margin-right: 0in; line-height: 115%; font-family: Calibri,sans-serif; margin-left: 0in; margin-bottom: 10.0pt; font-size: 11.0pt;">Abstract: We consider a joint asymptotic framework for studying semi-nonparametric models where (finite dimensional) Euclidean parameters and (infinite dimensional) functional parameters are both of interest. A class of generalized partially linear models is used as a prototypical example (under the penalized estimation). We first show that the Euclidean estimator and (point-wise) functional estimator, which are re-scaled at different rates, jointly converge to a Gaussian vector. This weak convergence result reveals a surprising joint asymptotics phenomenon: these two estimators become asymptotically independent while the Euclidean estimator achieves the semiparametric efficiency bound. Our first goal is to provide deep theoretical insights into the above phenomenon. A semi-nonparametric version of the Wilks phenomenon is unveiled as an interesting by-product. Our second goal is to develop more useful joint global inference for the same class of models. In particular, we find that "the inclusion of a faster convergent parametric estimator indeed affects the nonparametric global/local inference." This conclusion is against the common intuition that the parametric term (given its faster convergence rate) can be treated as if it were known. In the end, I will discuss a few open problems in this new field.</p>Njkmcdonbzuniga13859947171876321ea2fc7182410VgnVCM100000c2b1d38d____once11112newnew/UMICH/stats/Home/News & Events/Statistics Seminar/Guang Cheng.pdfGuang Chen, Ph.D. Associate Professor, Department of Statistics, Purdue University