Fall 2010

** ********** ****Announcements**** **************

· Please read the materials that I assign in class if you have time.

· The midterm exam will be on Wednesday, Nov.3, in class. It will cover the materials from the first 4 weeks. One ‘cheat sheet’ is allowed.

· Oct 25: we covered an example from Efron and Hinkley paper (below) on observed Fisher information.

· Nov 24 office hour ends early at 2:45.

**Overview:** This course uses the reference (not text –
note) book by Lehmann and Casella
(see list of topics below). Most homework problems come from the book. In
addition, reference papers often contain important and required materials, and
other reference books should help understanding.

Although I do not take attendance, past experience showed that missing more than occasional lectures impaired learning substantially. This is not a course meant for ‘study-it-yourself’.

**Topics:**

· Probability preparation

· Location-scale families

· Exponential families and sufficient statistics

· Convex loss functions

· UMVU estimators (intro only)

· Information inequality

· Convergence in probability and law

· MLE: consistency, asymptotic normality and efficiency

· Observed Fisher information

· More on likelihood theory (multiple roots etc.)

· Extension beyond i.i.d.; random effects models and EM algorithm

· Bayes estimators

· Asymptotic equivalence of Bayes estimator and MLE

**Lecture:** MWF 1:00-1:50pm, AP&M 5402

**Instructor: **Ronghui (Lily) Xu

**Office:** APM 5856

**Phone:** 534-6380

**Email: **rxu@ucsd.edu

**Office Hours:**

**W: **2:00pm - 2:50pm

Or, by appointment (you can email me to set up an appointment).

**Teaching Assistant:**

Will Garner (click link to office hours, homework and exam solutions)

**Office: **APM 6422

**Email: **wgarner@math.ucsd.edu

**Reference book:**

Lehmann and Casella, "Theory of Point Estimation"

**Other reference books:**

1. Bickel and Doksum, “Mathematical Statistics: basic ideas and selected topics”;

2. Casella and Berger, “Statistical Inference”;

3. DusGupta, "Asymptotic Theory of Statistics and Probability";

4. Barndorff-Nielsen and Cox, “Inference and Asymptotics”;

5.

**Reference papers:**

1.Efron, B. and Hinkley, D.V.
(1978) Assessing the accuracy of the maximum likelihood estimator: observed
versus expected Fisher information. *Biometrika*,
**65**, 457-487.

2.Laird,
N.M. and Ware, J.H. (1982) Random-effects models for longitudinal data. *Biometrics*,
**38**, 963-974.

3.Cnaan, A., Laird, N.M. and Slasor,
P. (1997) Using the general linear mixed model to analyse
unbalanced repeated measures and longitudinal data. *Statistics in Medicine*,
**16**, 2349-2380.

** **

**Homework: **due mostly by ^{th} floor of AP&M building:

Week 1,2 (due 10/11): Chapter 1 problem 1.2, 1.4, 2.2, 3.2, 4.2, 4.13(b), 5.1, 5.2

Also: for the handout datasets, describe the scientific questions(s) that might be of interest, and name the parameter(s) that you’d like to estimate.

Week 3,4 (due 10/25): Chapter 1 problem 7.9, 7.10(a), 5.6(a); Chapter 2 problem 5.5, 5.6, Chapter 1 problem 8.1, 8.4, 8.17, 8.24, Chapter 6 problem 3.2, 3.13

Week 5 (not due): Chapter 6 problem 3.17, 4.6

Week 6,7 (due 11/15): Chapter 6 problem 5.1(a), 5.3(b), 6.9, 6.5(ab), 6.11

Read Chapter 6 Examples 6.1, 6.3, schizophrenia example in paper by Cnaan et al. above, Example/definition/theorem/corollary 6.5-6.8, 7.2-7.3

Week 8,9 (due 11/29): Chapter 6 problem 4.15 (2 typos in book: ‘unknown’ variance; sigma^2_A and sigma^_U);

Show that under the marginal model formulation (2) of the Laird-Ware model, if the V_i’s are known, the MLE is the WLS estimator given in class.

Week 10 (not due): Chapter 4 problem 1.3, 1.6

**Grading:** 40% Homework + 30% Midterm + 30% Final