Statistics 242b
Statistical Inference
(Statistics 242/542)
Spring 1996
Instructor: David Pollard (pollard@stat.yale.edu; http://www.stat.yale.edu/~pollard)
Office: Statistics Department, 24 Hillhouse Avenue.
Phone: 432-0666
Office hours: Monday 12:00--2:00
Teaching Assistant: Alex Thiry (thiry@stat.yale.edu)
Office hours: Please email to arrange office hours
Prerequisites:
Statistics 241a and linear algebra, at
the level of Math 220.
Grading:
Problem set about every two weeks, counting for 40% of final grade
Midterm test, counting for a token 10% of final grade
Final exam, counting for 50% of final grade
Homework policy:
Late homework accepted only with a Dean's
note. No work accepted after distribution of solution sheet.
Aim of the course
"Principles of statistical analysis: maximum likelihood, sampling
distributions, estimation, confidence intervals, tests of
significance, regression, analysis of variance, and the method of
least squares."
Text:
Rice "Mathematical Statistics and Data Analysis"
I hope to cover most of the material in Chapters 7 to 12, and 14, of Rice, with
some material from Chapters 13 and 15 if time permits. I would expect to
devote about the same amount of time to each topic as I did when I
last used the Rice text, in 1990, but with some
modifications to allow for more discussion of computing issues. I
strongly recommend that students who take 242 also enrol in
Statistics 200b.
Click Very little technical material, but good for discussion of subtle
ideas. Fun to read.]
Bickel and Doksum "Mathematical Statistics: Basic Ideas and
Selected Topics" (Holden-Day, 1977)
[
A text at the next level up from 242. A good source for more detailed
information.]
Chambers, Cleveland, Kleiner, and Tukey "Graphical Methods for
Data Analysis" (Wadsworth, 1983)
[ Good discussion of topics such as Q-Q plots.]
Tanur, Mosteller, Kruskal, Link, Pieters, and Rising "Statistics:
A Guide to the Unknown" (Holden-Day, 1972).
[A collection of short articles that illustrate many aspects of
statistics. I might steal from it.]
Stuart "Basic Ideas of Scientific Sampling" (Griffin, 1968).
[Good discussion of sampling, with lots of simple numerical
examples.]
Material covered in 1990
Here is the breakdown of the course for Spring 1990. I intend to
follow the same order of topics this year, but with some
reapportionment of time spent on each chapter.
Survey sampling (Chapter 7; Lectures 1-6)
- Simple random sampling (with and without replacement); normal approximations;
variance corrections; confidence intervals for mean; estimation of
variance.
- Ratio estimators
- Stratified sampling; optimal allocation.
Estimation (Chapter 8; Lectures 7-11)
- Method of moments (for fitting negative binomial); general method
of moments (M-estimators) with normal approximation; confidence
intervals; MLE as optimal M-estimator.
- Information inequality; MLE in cases like uniform(0,theta); MLE
for normal distribution; negative binomial MLE; sufficiency.
- Special supplement on generalized method of moments
Hypothesis testing and goodness-of-fit (Chapter 9; Lectures 12-17)
-
Type 1 and type 2 errors; power functions; Neyman-Pearson lemma
- Chi-square test; likelihood ratio test
- Q-Q plots etc
There was some overlap between the last topic for Chapter 9 and
the topics for Chapter 10.
Summarizing data (Chapter 10; Lectures 18-20)
-
Histograms and density estimators; kernel estimation.
- Estimates of location; median; trimmed mean; more on M-estimators.
Comparing two samples (Chapter 11; Lectures 21-24)
-
Facts concerning multivariate normal; t-tests; nonparametric tests
Analysis of variance (Chapter 12; Lectures 25-30)
-
One-way ANOVA; geometric interpretation; generalized ANOVA table;
least squares
-
Two-way tables (Box-Cox survival data); transformations and plots
Regression (Chapter 14; Lectures 31-34)
-
Fit a+bx; estimation of linear functions of parameters; variances; t-tests
-
Multiple regression; more least squares.
- Material that is now covered in
Statistics 312a.
Decision theory and Bayesian inference (Chapter 15; Lectures 35-36)
-
Posterior distributions.
- Betting against confidence intervals, and other puzzles.