STATS 7059 - Mathematical Statistics
North Terrace Campus - Semester 1 - 2014
General Course Information
Course Code STATS 7059 Course Mathematical Statistics Coordinating Unit Statistics Term Semester 1 Level Postgraduate Coursework Location/s North Terrace Campus Units 3 Contact Up to 3 hours per week Prerequisites MATHS 1012 Assumed Knowledge STATS 2107 Course Description Statistical methods used in practice are based on a foundation of statistical theory. One branch of this theory uses the tools of probability to establish important distributional results that are used throughout statistics. Another major branch of statistical theory is statistical inference. It deals with issues such as how do we define a "good" estimator or hypothesis test, how do we recognise one and how do we construct one? This course is concerned with the fundamental theory of random variables and statistical inference.
Topics covered are: calculus of distributions, moments, moment generating functions; multivariate distributions, marginal and conditional distributions, conditional expectation and variance operators, change of variable, multivariate normal distribution, exact distributions arising in statistics; weak convergence, convergence in distribution, weak law of large numbers, central limit theorem; statistical inference, likelihood, score and information; estimation, minimum variance unbiased estimation, the Cramer-Rao lower bound, exponential families, sufficient statistics, the Rao-Blackwell theorem, efficiency, consistency, maximum likelihood estimators, large sample properties; tests of hypotheses, most powerful tests, the Neyman-Pearson lemma, likelihood ratio, score and Wald tests, large sample properties.
Course Coordinator: Associate Professor Robb Muirhead
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning OutcomesOn successful completion of this course students will be able to:
1. demonstrate knowledge of, and properties of, statistical models in common use,
2. understand the basic principles underlying statistical inference (estimation and hypothesis testing),
3. be able to construct tests and estimators, and derive their properties,
4. demonstrate knowledge of applicable large sample theory of estimators and tests.
University Graduate Attributes
This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:
University Graduate Attribute Course Learning Outcome(s) Knowledge and understanding of the content and techniques of a chosen discipline at advanced levels that are internationally recognised. all An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems. all A proficiency in the appropriate use of contemporary technologies. all A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life. all
Required ResourcesA set of lecture notes will be provided.
Recommended ResourcesOnline (MyUni) resources:
1. Mathematical Statistics III Lecture Notes, by P. Solomon and G. Glonek.
2. Introduction to Statistical Theory, by R. Muirhead and J. Sun.
1. Mathematical Statistics and Data Analysis (3rd ed.), by J. A. Rice, Duxbury Press.
2. Statistical Inference (2nd ed.), by G. Casella and R. L. Berger, Duxbury Press.
Online LearningThis course uses MyUni exclusively for providing electronic resources: lecture notes, assignments, solutions, etc. Students are advised to make extensive use of these resources.
Learning & Teaching Activities
Learning & Teaching ModesThis course relies on lectures as the primary delivery mechanism for the material. Tutorials supplement the lectures by providing exercises and example problems to enhance the understanding obtained through lectures. A sequence of written assignments provides assessment opportunities for students to gauge their progress and understanding.
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
Activity Quantity Workload Hours Lectures 30 90 Tutorials 5 18 Assignments 5 48 Total 156
Learning Activities SummaryLecture outline
1-3: Review of probability, random variables, density and mass functions, expectation, mean, variance
4-6: Standard probability distributions (statistical models) and their properties
6-7: Exponential families of distributions; distribution and expectation of a function of a random variable
8-11: Joint distributions, covariance, correlation, independence of random variables, distributions of functions of jointly distributed random variables, conditional distributions, conditional means and variances
12-14: Sums of independent random variables, transformations of two or more jointly distributed random variables
14-15: Random vectors, the multivariate normal distribution and properties
16-19: Modes of convergence, laws of large numbers, central limit theorem, Jensen's inequality
20-22: Random samples, the chi-square, t, and F distributions and their roles in normal sampling, basic concepts of statistical inference, the likelihood principle, sufficient statistics
23-25: Basic concepts of estimation; method of moments, maximum likelhood, large sample properties (consistency, asymptotic normality), mean square eror, Rao-Blackwell theorem
26-27: Fisher information, the Cramer-Rao inequality, confidence intervals and properties
28-30: Hypothesis testing, types of errors, p-value, power, Neyman-Pearson lemma, uniformly most powerful tests, likelihood ratio tests, Wald tests, score tests
Tutorial outline: Tutorial material will be integrated into the lecture and assignment material
The University's policy on Assessment for Coursework Programs is based on the following four principles:
- Assessment must encourage and reinforce learning.
- Assessment must enable robust and fair judgements about student performance.
- Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
- Assessment must maintain academic standards.
Component Weighting Objective Assessment Assignments 30% all Exam 70% all
Assessment Related RequirementsAn aggregate score of at least 50% is required to pass the course.
Assessment DetailFive equally weighted (6% each) assigments, due on Friday by 4 pm at the end of weeks 3, 5, 7, 9, 12. The assignments will be distributed on Monday of weeks 2, 4, 6, 8, 10.
Submission1. All written assignments are to be submitted to the designated hand-in box in the School of Mathematical Sciences with a signed cover sheet attached.
2. Late assignments will not be accepted.
3. Assignments will have a two-week turn-around time for feedback to students.
Grades for your performance in this course will be awarded in accordance with the following scheme:
M10 (Coursework Mark Scheme) Grade Mark Description FNS Fail No Submission F 1-49 Fail P 50-64 Pass C 65-74 Credit D 75-84 Distinction HD 85-100 High Distinction CN Continuing NFE No Formal Examination RP Result Pending
Further details of the grades/results can be obtained from Examinations.
Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.
Final results for this course will be made available through Access Adelaide.
The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.
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