This class will cover finite sample theory of statistical inference – including estimation, hypothesis testing, and confidence intervals – and elementary large sample theory. Specific topics (depending on time may or may not be able to cover all but aim to) include: statistical models; sufficiency; applications to exponential families, group families, and nonparametric families; minumum risk unbiased estimation; minimum risk equivariant estimation; Cramer-Rao Inequality; loss and risk functions; Bayes estimation; minimax estimation; admissibility; shrinkage estimators; Neyman-Pearson theory for hypothesis testing; confidence intervals; uniformly most powerful test and uniformly most accurate confidence intervals; asymptotic relative efficiency; maximum likelihood estimation; Wald, score, and likelihood-ratio tests; delta method; asymptotic distribution of quantiles and trimmed means.

Acknowledgement: This course contains materials such as lecture slides, homework and datasets that were developed or adapted from STA210A at UC Berkeley by Michael Jordan and Will Fithian, STA300A at Stanford by Dominik Rothenhaeusler.

STA 250 or STA 611, STA 711, linear algebra, undergraduate level real analysis

Location: Old Chem 025

Time: Monday and Wednesday 3:30pm - 4:45pm

Email: yuansi.chen at duke.edu

Office hours: MW 4:45-5:30 or by appointment in 223B

Christine Shen

Email: yueming.shen@duke.edu

Office hours: Tuesday 1:00-2:00, Friday 2:20-3:20 in Old Chem 203B,

Main text:

Keener,

*Theoretical Statistics: Topics for a Core Course*, Springer 2010Lehmann and Casella,

*Theory of Point Estimation*, Springer 1998Lehmann and Romano,

*Testing Statistical Hypotheses*, Springer 2005

Undergraduate review textbook:

Sta711 review textbook:

Other resources:

Statistical Decision Theory and Bayesian Analysis. 2nd Ed. Berger, 1985

Tentative, please refresh for the latest version

Date | Required Reading | Topic | Slides | Other |

Jan. 11 | Chap.1.1, 1.2 of Lehmann and Casella / Chap 3.1 of Keener | Course introduction | lecture01 | review 711 |

Jan. 16 | - | No class | holiday | |

Jan. 18 | Chap. 2 of Keener | Exponential families | lecture02 | hw00 due & hw01 out |

Jan. 23 | Chap. 2 - 3.4 of Keener | Sufficient statistics | lecture03 | |

Jan. 25 | Chap. 3.4 - 3.6 of Keener | Completeness, Basu thm | lecture04 | hw01 due & hw02 out |

Jan. 31 | Chap. 3.6 - 4.1 of Keener | Rao-Blackwell thm, UMVU | lecture05 | |

Feb. 01 | Chap. 4.2, 4.5, 4.6 of Keener | More on bias, Information inequality | lecture06 | hw02 due & hw03 out |

Feb. 06 | Chap. 10.1 of Keener | Equivariance | lecture07 | |

Feb. 08 | Chap. 10.2 of Keener | Equivariance estimation | lecture08 | hw03 due & hw04 out |

Feb. 13 | Chap. 7.1, 7.2 of Keener | Bayesian estimation | lecture09 | |

Feb. 15 | Chap. 4.1 of Lehmann and Casella | Bayes pros and cons | lecture10 | hw04 due & hw05 out |

Feb. 20 | Chap. 15.1, 11.1-2 of Keener | Empirical Bayes and Hierarchical Bayes | lecture11 | sample midterm |

Feb. 22 | Chap. 5.1-2 of Lehmann and Casella | Minimax optimality | lecture12 | hw05 due & hw06 out |

Feb. 27 | Midterm review | |||

Mar. 01 | Midterm | |||

Mar. 06 | Chap. 5.1-2 of Lehmann and Casella | Minimax optimality + Minimax estimators | lecture13 | |

Mar. 08 | Chap. 8.1-2 of Keener | Large sample theory basics | lecture14 | hw06 due & hw07 out |

Mar. 13 | Spring break | |||

Mar. 15 | Spring break | |||

Mar. 20 | Chap. 8.3, 8.5, 9.2, 9.3 of Keener | Asymptotic of MLE | lecture15 | |

Mar. 22 | Chap. 8.3, 8.5, 9.2, 9.3 of Keener | Asymptotic of MLE, cont | hw07 due & hw08 out | |

Mar. 27 | Chap. 12.1-4 of Keener | Hypothesis testing & Neyman-Pearson paradigm | lecture16 | |

Mar. 29 | Chap. 12.3-7 of Keener | UMP | lecture17 | hw08 due & hw09 out |

Apr. 03 | Chap 3.6, 3.7 of Lehmann and Romano | UMP in two-sided testing? | lecture18 | |

Apr. 05 | Chap 3.8 of Lehmann and Romano | Least favorable distributions | lecture18-19 | hw09 due & hw10 out |

Apr. 10 | Chap 4 of Lehmann and Romano | UMPU | lecture20 | |

Apr. 12 | Chapt. 13.1-3 of Keener | UMPU in multiparam exp family | lecture21 | hw10 due & hw11 out |

Apr. 17 | Chapt. 14.5-8 of Keener | Testing in general linear model | lecture22 | |

Apr. 19 | Chapt. 17.1-4 of Keener | Large-sample LRT & final review | lecture23 | hw11 due |

Apr. 24 | graduate reading | |||

Apr. 26 | graduate reading | |||

May. 01 | final exam | |||

Attend lectures

Complete required reading in textbook

Complete weekly homework (posted on Sakai)

Midterm (in class on March 1)

Final (9:00-12:00 on May 1)

Homework (25%) + Midterm (25%) + Final (45%) + Participation (5%). Participation includes lecture attendance, lecture scribing and discussion participation on Sakai.

**Late homeowork policy**: Homework turned one minute late but on the due day will be counted as one day late. The next day will be two days late, etc. No homework more than two full days (48 hours) late will be accepted. Each late day will result in a one-level down-grade (10% off) of that homeowork.**Regrade requests**on Gradescope within 2 daysDrop the HW with the lowest score for final grade

**Exam policy**: no makeup exams

I understand that the electronic recording of notes might be important for class and so computers will be allowed in class. Please refrain from using computers for anything but activities related to the class. Phones are prohibited as they are rarely useful for anything in the course. Eating and drinking are allowed in class but please refrain from it affecting the course.

Duke University is a community dedicated to scholarship, leadership, and service and to the principles of honesty, fairness, respect, and accountability. Citizens of this community commit to reflect upon and uphold these principles in all academic and non-academic endeavors, and to protect and promote a culture of integrity. Cheating on exams and quizzes, plagiarism on homework assignments and projects, lying about an illness or absence and other forms of academic dishonesty are a breach of trust with classmates and faculty, violate the Duke Community Standard, and will not be tolerated. Such incidences will result in a 0 grade for all parties involved as well as being reported to the Office of Student Conduct. Additionally, there may be penalties to your final class grade. Please review the Duke Academic Dishonesty policies.

Students with disabilities who believe they may need accommodations in this class are encouraged to contact the Student Disability Access Office at (919) 668-1267 as soon as possible to better ensure that such accommodations can be made.