Asymptotic Tools

Spring 2020

Time and Place |
TuTh 10:35-11:50 in 010 Life Sci | |

Instructor |
David Hunter
310 Thomas dhunter@stat.psu.edu Office hours: W 4:00-5:00 in 310 Thomas | |

Teaching Assistant |
Ying Zhang
301 Thomas yuz390 [at] psu [dot] edu Office hours: M 2:00-3:00 in 333 Thomas | |

Purpose |
This course will introduce students to some of
the important statistical ideas of
large-sample theory without requiring any mathematics beyond calculus
and linear algebra. In particular, no measure theory is required.
However, a basic understanding of statistics at the level
of Statistics 513-514 will be assumed. Furthermore, the level
of mathematical rigor will be high even if the level of
the mathematics is not. In particular, understanding and writing
proofs will be vital. | |

Intended Audience |
This course is required
for all second-semester Ph.D. students in statistics.
If you think you might be interested in taking
it but you're not sure, please
don't hesitate to come and talk to me or send me an email.
I welcome anyone interested in this subject. | |

Lecture notes |
Lectures will be based primarily on a set of lecture notes available at http://personal.psu.edu/drh20/asymp/lectures/. I may be revising these notes throughout the semester, so if you have seen versions of these notes from previous semesters, be advised that changes may have taken place. | |

Optional Textbook #1 |
T. S. Ferguson, A Course in Large Sample Theory
(Chapman and Hall, 1996)
I highly recommend this great book, particularly for those of you who are pursing a PhD in statistics. First of all, it's paperback so it's not as expensive as most hardcover statistics textbooks. Second, it has the very unusual yet enormously helpful feature that the exercises are all fully worked in the appendix (the best way to learn this stuff is to work problems, and with the solutions available to guide you when you get stuck, this book is ideal for self-study). Third, it is very concisely written, managing to pack a lot more information into the average page than the Lehmann book (partly this is because it is written almost entirely in the multivariate setting, so there is no separate treatment of the multivariate case). Fourth, it is divided into small, self-contained chunks, making it possible to sample different topics in almost any order you wish. All of these features make it a terrific reference book to have on your shelf. You may wonder why, if it's such a great book, I don't use it as the main textbook for this course. The reason is that its mathematics is a bit more advanced than I'd like, since the whole point of this course is to present as much statistics as possible without relying on too deep a mathematical background. | |

Optional Textbook #2 |
E. L. Lehmann, Elements of Large-Sample Theory
(Springer, 1999)
I really like this book, especially for the level of this class. It is statistically rigorous without being overly mathematical and it contains many enlightening examples and exercises. It appears that this book is out of stock and may be hard to obtain. This won't be a serious problem, since the course notes will be available regardless. I used to require this book in this course, and I've compiled a lengthy list of errata for it. | |

Computing |
Computing will play a large role in the homework
assignments. The software I'd recommend using is R, although I
won't require any particular package or language. You can probably
get by with Minitab if you're very comfortable with it, and
packages such as Matlab, Maple, or Mathematica or languages such as C or
Fortran should be okay as well--however, before deciding to use one
of these last 5, be sure you can obtain functions like the standard
normal cdf and inverse cdf as well as random deviates from not just
the uniform but all the common distributions as well.
You will also need to be able to produce graphics such as
histograms and plots of functions.
If you're not currently familiar with R,
I strongly encourage you
to visit the RStudio web site at
rstudio.com/ and download
RStudio for free. There are many sources of help available online to
get started with learning R.
| |

Grading |
There will be two midterms (15% each), a comprehensive final exam (20%), and weekly homework (50%). The exams will be closed-book but you'll be allowed to bring a page or two of notes. This arrangement is similar to the rules for the qualifying review exams in May, which are comprised partly of questions on asymptotics. | |

Academic Integrity Policy |
All Penn State and Eberly College of Science policies regarding academic integrity apply to this course. See http://science.psu.edu/current-students/Integrity/Policy.html for details. | |

Code of Mutual Respect |
As the instructor for this course, I strongly endorse the Eberly College Code of Mutual Respect and Cooperation. I intend to adhere to these tenets in my dealings with students and I hope that students will reciprocate in their interations with all other students, teaching assistants, learning assistants, and me. The code may be found online at http://science.psu.edu/climate/code-of-mutual-respect-and-cooperation/Code-of-Mutual-Respect%20final.pdf/view. | |

Disability Accommodation Statement |
Penn State welcomes students with disabilities into the University's educational programs. The Student Disability Resources (SDR) Web site at http://equity.psu.edu/sdr/disability-coordinator provides contact information for every Penn State campus. At University Park, the SDR office is in 116 Boucke. In order to receive consideration for reasonable accommodations, please contact SDR and provide documentation as explained in the guidelines at http://equity.psu.edu/sdr/guidelines | |

Counseling and Psychological Services Statement |
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Educational Equity/Report Bias Statement |
Students who believe they have experienced or observed a hate crime, an act of intolerance, discrimination, or harassment that occurs at Penn State are urged to report this incident as outlined on the University's Report Bias webpage at http://equity.psu.edu/reportbias/. |