Large Sample Theory Homework Online

Statistics 210A: Theoretical Statistics (Fall 2017)

Course Information

  • Prof. Will Fithian (Instructor)

    • Evans 301

    • Office Hours: Tu 2-3, W 11-12 (or by appointment)

  • Xiao Li (GSI)

    • Evans 428

    • Office Hours: Tu 10-11, Th 3:30-4:30 (location TBD)

  • Lectures TuTh 12:30-2, Wheeler 222

  • Final Exam Th Dec 14, 3-6pm, location TBD

  • Syllabus

  • Announcements, homework, handouts at bCourses

  • Piazza discussion site for technical questions (no homework spoilers!)

Materials

Materials from class:

  • Aug. 29: demo of exponential tilting

  • Sep. 21: demo of Bayesian inference for the Beta-Binomial distribution

  • Oct. 3: demo of Bayes, hierarchical Bayes, and James-Stein

Assignments:

Content

Stat 210A is Berkeley's introductory Ph.D.-level course on theoretical statistics. It is a fast-paced and demanding course intended to prepare students for research careers in statistics.

Topics:

  • Statistical decision theory, frequentist and Bayesian

  • Exponential families

  • Point estimation

  • Hypothesis testing

  • Resampling methods

  • Estimating equations and maximum likelihood

  • Empirical Bayes

  • Large-sample theory

  • High-dimensional testing

  • Multiple testing and selective inference

Prerequisites:

  • Linear algebra

  • Real analysis

  • One year of upper-division probability and statistics

References

All texts are available online from Springer Link.

Main text:

Supplementary texts:

Grading

Your final grade is based on:

  • Weekly problem sets: 50%

  • Final exam: 50%

Lateness policy: Late problem sets will not be accepted, but you will get to drop one grade.

Collaboration policy: For homework, you are welcome to work with each other or consult articles or textbooks online, but

  1. You must write up the problem by yourself.

  2. You may NOT consult any solutions for previous iterations of this course.

  3. If you collaborate or use any resources other than course texts, you must acknowledge your collaborators and the resources you used.

Academic integrity: You are expected to abide by the Berkeley honor code. Violating the collaboration policy, or cheating in any other way, will result in a failing grade for the semester.

Reading Assignments

Date Reading
Aug. 24 Chap. 1 and Sec. 3.1 of Keener
Aug. 29 Chap. 2 of Keener
Aug. 31 Chap. 2 and Sec. 3.2 of Keener
Sep. 5 Secs. 3.4, 3.5, and 3.6 of Keener
Sep. 7 Secs. 3.6 and 4.1 of Keener
Sep. 12 Secs. 4.1 and 4.2 of Keener
Sep. 14 Secs. 4.5 and 4.6 of Keener
Sep. 19 Secs. 7.1 and 7.2 of Keener
Sep. 21 Secs. 7.1 and 7.2 of Keener
Sep. 26 Secs. 7.2 and 11.1 of Keener
Sep. 28 Secs. 7.2 and 11.1 of Keener
Oct. 3 Secs. 11.1, 11.2 and 9.4 of Keener
Oct. 5 Secs. 12.1, 12.2, 12.3 and 12.4 of Keener
Oct. 10 Secs. 12.3, 12.4, 12.5, 12.6 and 12.7 of Keener
Oct. 12 Secs. 13.1, 13.2, and 13.3 of Keener
Oct. 17 Secs. 13.1, 13.2, and 13.3 of Keener
Oct. 19 Secs. 13.1, 13.2, and 13.3 of Keener
Oct. 24 Secs. 14.1, 14.2, 14.4, 14.5, and 14.7 of Keener
Oct. 26 Secs. 8.1, 8.2, and 8.3 of Keener
Oct. 31 Secs. 8.3 and 8.4 of Keener
Nov. 2 Secs. 8.5, 9.1, and 9.2 of Keener
Nov. 7 Secs. 9.1, 9.2, and 9.3 of Keener
Nov. 9 Secs. 9.1, 9.2, and 9.3 of Keener
Nov. 14 Secs. 9.5 and 9.7 of Keener
Nov. 16 Secs. 19.1 – 19.3 of Keener; 15.1 – 15.4 of Lehmann & Romano
Nov. 21 Lecs. 2 and 3 of Candes
Nov. 23 No class. Happy Thanksgiving!
Nov. 28 Lec. 6 of Candes
Nov. 30 Lecs. 8 and 9 of Candes

The practice of advanced statistics normally requires the use of sophisticated software, not due to theoretical complexity but rather to sheer volume and repetition of required calculations. Without computers, advanced statistical number crunching would be too time consuming, especially with large data sets.

A course in advanced statistics will most likely follow the experience and particular interests of the professor. It is safe to say, however, that whatever material is covered will most likely involve a sophisticated treatment of many of the following topics:

  • Descriptive statistical techniques
  • Probability theory
  • Random variables and probability distributions
  • Bivariate probability distributions
  • Discrete parametric probability distributions
  • Continuous parametric probability distributions
  • Sampling and the sampling distribution of a statistic
  • The chi-square, student's t, and Snedecor's F distributions
  • Point estimation and properties of point estimators
  • Interval estimation and confidence interval estimates
  • Tests of parametric statistical hypotheses
  • Nonparametric statistical techniques
  • Testing goodness of fit
  • Testing goodness of fit : contingency tables
  • Bivariate linear regression and correlation


First and foremost, students should take advantage of MIT's Open Courseware that offers the highest quality advanced statistics courses online (for free), including Mathematical Statistics and Topics in Statistics: Nonparametrics and Robustness. Quite a selection of good books is available on advanced statistics, many of which can be found on Google Books and Amazon.com. Students should also follow Springer's Advances in Statistical Analysis and Advances in Data Analysis and Classification, as well as Pushpa Publishing House's Advances and Applications in Statistics, and Scientific Advances Publishers' Journal of Statistics: Advances in Theory and Applications.

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