Emanuel Parzen and a Tale of Two Kernels Prepared for the Journal of Time Series Analysis

I was Manny Parzen’s fifth student, according to the Mathematical Genealogy Project, receiving my PhD under his supervision in 1966, and remaining at Stanford with him for a postdoc, leaving for the University of Wisconsin-Madison in 1967, where I remain as I write. To be Manny’s PhD student at Stanford in the 60’s was nothing short of bliss. Many was full of ideas, the weather was warm and sunny, sometimes classes were held on the grass in front of the old Sequoia Hall with Reproducing Kernel Hilbert Spaces on the improvised blackboard. A lovely, elegant dinner at their Stanford home that Manny and Carol threw for a group of graduate students bring back fond memories. Manny and Carol remained lifelong friends. Manny launched me on a 50 year academic year, buttressed by what I learned about RKHS from him in those days. In this article I first describe many fond memories over the years, and then present some technical results and thoughts relating to RKHS, Parzen density estimates, Statistical Machine learning and related topics. 1 Scholar, teacher, friend 1.1 Manny as PhD advisor In 1962 I was a single mom working at a D. C. area think tank and also working towards an MS at the University of Maryland-College Park when I read Research supported in part by NSF Grant DMS-1308847 and a Consortium of NIH Institutes under Award Number U54AI117924