Some of Nonparametric Statistics

Author

Karl Gregory

Preface

Map of topics. Photo is of Mount Everest.

This is an eBook of notes for a graduate-level nonparametric statistics course I have taught a few times at the University of South Carolina.

You see a map above charting the topics treated in this book, which I have entitled “Some of Nonparametric Statistics”, in a not-so-subtle riff on the title of Larry Wasserman’s famous book “All of Nonparametric Statistics”; see Wasserman (2006). I have intentionally left the summit unlabeled to emphasize that I do not presume to have covered, in any sense, “all” of nonparametric statistics—not all that has been to this date learned, nor indeed all that is yet to be learned in this realm.

I must be forgiving, nevertheless, of Wasserman’s presumption, as these notes contain much that is adapted from his work, which served as a compass during my own journey through these topics. Another pointer to True North was the book “Introduction to Nonparametric Estimation” by Alexander Tsybakov, see Tsybakov (2008).

I find myself indebted to Tsybakov not only for bringing into the world such a book, but also indebted to him personally for the great forbearance he demonstrated on an occasion which he may remember to this day (or perhaps not). I, a post-doc at the Universität Mannheim, was put in charge of finding a room in which the visiting Alexander Tsybakov, traveling from Paris, would make a presentation on his latest work to the students, post-docs, and faculty composing our research group. In the callowness of youth, I asked our secretary to book a room, telling her the speaker wanted a whiteboard, as it was to be a talk in the tradition of the Chalkboard Talk long celebrated by mathematicians of the Continent. Tragically, when we arrived at the room, we found that it possessed not a vast wall-mounted whiteboard as I had imagined, but rather an easel-mounted one about the size of a bathroom mirror. So the venerable Alexander Tsybakov wrote, and then erased, and then wrote and erased for an hour, presenting all the while quite eloquently in spite of the diminutive canvas on which he was forced to cram his notations. To his great credit he never expressed annoyance and was very kind to me throughout his visit. So, let warm appreciations emanate to the man Tsybakov for his book as well as for his equanimity.

Now let us begin our climb out of the vale onto the snowy heights…