Text: Statistical Inference by George Casella & Roger L. Berger

     Other References:

         Introduction to Mathematical Statistics Hogg & Craig

         Statistical Inference Garthwaite, Jolliffe & Jones

Course Description: Statistics is a very broad subject, with applications in a vast number of different fields. At heart it is an applied subject, but it would be unsatisfactory if each application had to be tackled separately, devising fresh techniques for each new problem. For this reason, a body of common statistical theory has been developed so that most problems can be tackled within the same framework.

There are three main subdivisions within statistics: efficient summarization, tabulation and graphical display of data; design of experiments; and statistical inference. Data summarization was historically the first major statistical activity. Experimental design is of crucial importance before data are collected. However, it is statistical inference which has seen most research and practical application in recent years, and it is inference which forms the direction of this course. There are three main types of inference, namely point estimation, interval estimation and hypothesis testing. In point estimation, for each unknown parameter of interest a single value is computed from the data, and used as an estimate of that parameter. Instead of producing a single estimate of a parameter, interval estimation provides a range of values which have a predetermined high probability of including the true, but unknown, value of the parameter. Hypothesis testing sets up specific hypotheses regarding the parameters of interest and assesses the plausibility of any specified hypothesis by seeing whether the observed data support or refute that hypothesis. Although hypothesis testing can often be artificial in the sense that none of the proposed hypotheses will be exactly correct (for example, exact equality of p for two species of birds is unlikely), it is often a convenient way to proceed and underlies a substantial part of scientific research.

The statistical community has during the last 10 years experienced a significant transformation stimulated by the technological developments in statistical computing environments, theoretical developments in stochastic based inference and simulation.

Students will learn how to use statistical software to facilitate the understanding of the foundations of multivariate analysis. Statistical packages will include SAS, S-Plus, and MatLab.

Topics to be covered include:

• Random Variables
• Distribution Functions
• Density and Mass Functions
• Transformations and Expectations
• Distributions of Functions of a Random Variable
• Moments and Moment Generating Functions
• Common Families of Distributions
• Discrete Distributions
• Continuous Distributions
• Exponential Families
• Multiple Random Variables
• Joint and Marginal Distributions
• Conditional Distributions and Independence
• Bivariate Transformations
• Covariance and Correlation
• Multivariate Distributions
• Inequalities and Identities
• Properties of a Random Sample
• Convergence Concepts
• Sampling from the Normal Distribution
• Properties of the Sample Mean and Variance
• The Derived Distributions: Student's t and Snedecor's F
• Order Statistics
• The Sufficiency Principle
• Sufficient, Ancillary, and Complete Statistics
• The Likelihood Principle
• Point Estimation
• Method of Moments
• Maximum Likelihood Estimators
• Sufficiency and Unbiasedness
• Consistency
• Hypothesis Testing
• Likelihood Ratio Tests
• Invariant Tests
• Error Probabilities and the Power Function
• Most Powerful Tests
• The Analysis of Variance
• Regression Analysis

Prerequisites: This course will suit recent students of MthSc 800 or the equivalence of MthSc 400/600 can be considered preparatory for those students interested in statistical inference. Prerequisites are a working knowledge of elementary probability rules.

Attendance Policy: All classes should be attended, but, if you are ill stay at home. I will accept e-mail or phone messages to that effect. Note that this does not exempt you from turning in homework/projects on time nor taking quizzes at their proposed times. Legitimate excuses must be offered with respect to the day(s) missed. Attendance will be monitored. It is to the instructors discretion whether an excuse is legitimate or not. Accordingly, the university's policy on religious holidays will be acknowledged and honored.

Tardy Professor Policy: If the instructor is more than 15 minutes late for any class you may leave.

Examination Policy:

There will be two 60 minutes in class examinations and a final examination. No makeup examinations will be given. Any student who misses an examination without a legitimate excuse,ie, a documented medical excuse, will receive a score of zero for that exam. A student with a legitimate excuse, will receive a final score based on all other class work. More than one missed exam with require withdrawal from the course and/or the receipt of a failing final grade.

Homework and/or Take Home Projects:

There will also be several homework sets and/or take home projects assigned from the text as well as from material covered during class. Although it is imperative that each student be completely comfortable with these assigned problems and projects, group study is encouraged.

Grading Policy: The two regular exams will count as 50% of the final grade, homework sets 10%, a applications project 20%, and the final exam 20%. The final exam will cover the more important topics covered during the semester.

Grading Scale:

A 100 - 90

B 89 - 80

C 79 - 70

D 69 - 60

F 59 -

This project is an opportunity to use the statistical techniques we have learned in class, to answer real-life questions. Projects should be done individually. Each student should:

• Choose a question or a topic that is of interest to them, and that can be answered via a designed experiment, an observational study, or by some statistical computing technique discussed in class.
• Report the findings.

You will have about 2 months to layout your project. Plan your time accordingly.

The grade will be based on the final report, which should contain the following items.

• A description of the question, and your reason for wanting to know the answer,
• A description of the techniques used,
• Analysis and illustration of the findings and conclusions.

Reports should be neatly typed, well-organized and attractive. Graphical displays (either computer-generated or hand-drawn) are encouraged. Generally, graphs are more effective if they are incorporated into the text, rather than hidden at the end of the report. You may also use a computer package to aid in the data analysis. If you do so, the results should be discussed in the text of your report, and the computer output itself may be included in an appendix.

A rough draft of the final report will be due approximately 2 weeks before the final report is due.

The project is worth 100 points. Grades will be based on:

Appropriate and correct procedures	50 pts
Well-written and attractive presentation	20 pts
Grammar, spelling and punctuation	20 pts
Complexity	10 pts

A project proposal (not graded) must be approved before the project is started. An approved proposal must be turned in with the final report. The proposal should state:

• The question and its motivation
• Plan for the project.
• Proposed analysis.

Due dates:

Proposal	November 4th
Rough draft	November 18th
Final Report	December 4th