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= Stats 300B: Theory of Statistics II
[http://www.stanford.edu/~jduchi/ John Duchi], Stanford University, Winter 2019
== Lectures
Tuesday and Thursday, 10:30 - 11:50 AM in Green Earth Sciences, Room 150.
== Course Staff Email Address
stats300b-win1819-staff_albatross_lists_duck_stanford_duck_edu (replace _albatross_ with @ and _duck_ with .)
== Instructor
John Duchi
- Office hours: Tuesdays and Thursdays, 3:00pm - 4:00pm, 126 Sequoia Hall.
== Teaching Assistants
Stephen Bates
- Office hours: Wednesday 4:00pm - 6:00pm, 220 Sequoia Hall.
Elena Tuzhilina
- Office hours: Mondays 10:00am -12:00pm, 420-286.
== Prerequisites
Stats 300A, Stats 310A.
== Texts
Required:
- [http://www.cambridge.org/catalogue/catalogue.asp?isbn=0521784506 /Asymptotic Statistics/], by van der Vaart, published by Cambridge University Press (ISBN-13: 9780521784504).
- [https://www.math.uci.edu/~rvershyn/papers/HDP-book/HDP-book.pdf High Dimensional Probability], by Roman Vershynin, to be published by Cambridge University Press.
Recommended:
- [http://link.springer.com/book/10.1007/b98854 /Theory of Point Estimation/], second edition,
by Lehmann and Casella, published by Springer (ISBN-13: 978-0387985022). # [doc/Errata-TPE2.pdf Errata].
- [http://link.springer.com/book/10.1007/0-387-27605-X /Testing Statistical Hypotheses/], third edition,
by Lehmann and Romano, published by Springer (ISBN-13: 978-0387988641). # [doc/Errata-TSH3.pdf Errata].
- [http://link.springer.com/book/10.1007/b98855 /Elements of Large Sample Theory/],
by Lehmann, published by Springer (ISBN-13: 978-0387985954).
== Grading
Your grade will be determined by scribing (5\%), weekly problem sets (60\%), and a final exam (35\%).
There will be weekly homework assignments throughout the course, which will count for 60\% of the grade. In effort to speed grading and homework return to you, we will grade homework problems and their sub-parts on a {0, 1, 2}-scale: 0 indicates a completely incorrect answer, 1 indicating approximately halfway correct, 2 indicating more or less correct. Everyone will be required to scribe at least one lecture (5\% of final grade), and (if necessary because of enrollment) we need some students to scribe two lectures, an additional scribed lecture will increase the percentage score S of your lowest homework to min{100, S + 50} (that is, by 50\%). There will be a final exam (either in class or take home, TBD by preference of class) worth 35\% of the grade.
# == Scribing
# In order to gain experience with technical writing, each student will be required to prepare scribe notes for a single lecture.
# After taking careful notes in class, the scribes for a given lecture will jointly prepare a LaTeX document (using [doc/scribe.sty this style file] and [doc/stats300a-fall15-scribe_template.tex this template]) *written in full prose* understandable to a student who may have missed class.
# The LaTeX document, along with any image or auxiliary files, should be submitted to the staff list *within two days* (excluding weekends) of the scribed lecture.
# After review, the scribe notes will be posted to the course website.
#
# Please sign up to scribe a specific lecture using [http://goo.gl/9WzkMt this spreadsheet].
#
# You will find the LaTeX scribe notes, style file, and any supporting image files from last year's edition of the course on the Stats 300A Coursework site (in the Materials section). You are encouraged to build off of and improve these notes rather than starting from scratch. Take special note of components of the notes that are inadequately explained or motivated and of material that has changed from last year.
#
# == Problem Sets
# Problem sets posted on the class website will be due in class on
# Thursdays at the start of lecture.
# If you are traveling, you may email your solution to one of the course staff in advance of the deadline.
# Ten percent of the homework value will be deducted for each day a homework is late.
# Exceptions will be made for documented emergencies.
# No credit will be given for homework submitted after solutions have been posted.
#
# After attempting the problems on an individual basis, each student may discuss a homework assignment with up to two classmates.
# However, each student must write up his/her own solutions individually and explicitly name any collaborators at the top of the homework.
#
# Please keep in mind the university [http://studentaffairs.stanford.edu/communitystandards/policy/honor-code honor code].
#
# == Final
# The final will be distributed online through the course website at 10AM on Mon. Dec. 7 and must be returned by 10AM on Weds. Dec. 9.
# (See the sample instructions on the practice final for more details on returning your solutions.)
# The final will cover all course material up to and including uniformly most powerful invariant tests (i.e., excluding our discussion of confidence regions in the final lecture).
# You may refer to your notes and your textbooks during the exam.
# You should not need to access the internet to answer any exam questions, and using the internet to search for solutions to these problems is cheating and in violation of our honor code.
# However, you may use Wikipedia to look up the form of unfamiliar distributions.
# Unless a problem explicitly states otherwise, you will be free to cite results proved in class, in the textbook, or on your problem sets.
#
== Course Overview
In this class, we will cover classical and not-so-classical techniques underpinning asymptotic statistics and
large sample theory. We will highlight a few of the big ideas, but the breadth of the subject by now is so
large that our treatment will necessarily be spotty.
== Outline
: {*Maximum likelihood estimation and models* (2 weeks)} Basic M-estimators, Asymptotic normality via the central limit theorem (CLT), Taylor-like models, The $\delta$-method
: {*Testing* (2 weeks)} Confidence intervals and $p$-values, Relative efficiency, Nonparametric tests, Worst-case alternatives
: {*U-statistics* (1 week)} Projections, Hoeffding and Hajek decompositions, One-sample and two-sample U-statistics, Degenerate U-statistics\
: {*Convergence of general random variables, processes, and uniform laws* (3 weeks)} Basic concentration inequalities, Uniform laws of large numbers and Glivenko Cantelli classes, Rademacher complexity, symmetrization, matrix concentration, Prohorov and Portmanteau theorems, Uniform central limit theorems
: {*Optimality, power, and contiguity* (2 weeks)} Contiguity and absolute continuity, Local asymptotic normality and quadratic mean differentiability, Limiting normal experiments and asymptotic power, Local asymptotic minimax theorems, Super-efficienty and the Hodges phenomenon