MAT3175 (Summer 2008)

INTRO. TO MATHEMATICAL STATISTICS

Limit theorems. Sampling distributions. Parametric estimation. Concepts of
sufficiency and efficiency. Neyman-Pearson paradigm, likelihood ratio tests.
Parametric and non-parametric methods for two- sample comparisons. Notions
of experimental design, categorical data analysis, the general linear model,
decision theory and Bayesian inference.

Prerequisites: MAT2125, MAT2141, MAT2375 (MAT3172 and or MAT4371 would be helpful)

Monday, 16:00 - 18:00    MCD120

Wednesday, 16:00 - 18:00    MCD120

Courses start May 1 and end July 1

Course Text: Introduction to Mathematical Statistics Sixth Edition by Hogg, McKean
and Craig

Professor:  David McDonald

Office Hours: Wednesday, 10:00 - 11:00, or by appointment.

email:  dmdsg@uottawa.ca

Midterm:  June 25th  Solution

Final Examination Tuesday July 22 13:00-16:00 MNT207 

Homework: Submit homework on Wednesdays.  Late assignments will not be
graded

Final Grade : If the grade on the final examination is less than 40% then
that is the final grade. If the grade on the final is  40% or more then the
final grade is calculated as:
Homework: 25%
Midterm Test:  25%
Final Examination:  50%
Total : 100%

NOTE: The midterm grade will be replaced by the grade on the final if the
later is higher. However, if you miss the midterm without a medical
certificate or an equivalent written justification then the midterm grade
will be zero and it won't be replaced.

First week: Reviewed joint densities and transformations of random variables.  Finished with a definition of a multivariate normal.

HW1 due May15 Solution

a) If X=(X_1,X_2,...X_n)' is a random vector. Define the covariance matrix S = E(X-EX)(X-EX)' Assuming the covariance is not singular show it is positive definite.

Show this  means it has positive eigenvalues s_i and orthonormal eigenvectors e_i.  Show that the covariance matrix can be written as s_1 e_1 e_1'+...s_n e_n e_n'. This is called the spectral decomposition.

Show that S (1/2)= (s_1)(1/2) e_1 e_1'+...s_n(1/2) e_n e_n is the square root of the covariance matrix.  Do the above operations for the matrix

                                                                    9     -2

                                                                    -2     6

Do 1.5.8,   2.1.1,     2.1.16,    2.2.1,    2.2.6

Second week: Finish Chapter 2 and recall facts from Chapter 3 including the multivariate normal

HW 2   due  May 21 Solution

 2.7.6, 3.4.10, 3.4.28, 3.5.1 (a), 3.6.10

Third week Started Bayesian statistics

HW3  due June 5th Solution

Do 3.4.30   3.5.17, 11.2.1, 11.2.3 plus the Bayesian problem given in class.

HW4 due  June 19 Solution
7.1.1, 7.2.1, 7.2.5, 7.4.6, 11.2.1 11.2.4

HW5 due July 16 Solution
8.1.10 8.2.4