- Lecturer
- Dr A. Xia, Melbourne, Semester 1.
- Syllabus
- Probability spaces and random variables, a measure theoretic approach.
Expectation and conditional expectation, distribution-free and distribution-based
approaches with applications to Mean Square Estimation and to Sufficient
Statistics. Modes of Convergence and Limit Theorems with applications to
Estimation and Hypothesis Testing. Martingales and their applications to
Statistics.
- Prerequisites
- Second year probability and some second year mathematics. Third year
subjects in probability/statistics/mathematics would be useful.
Generic
skills
- References
References
- Hogg and Craig (1970) Introduction to Mathematical Statistics,
Macmillan, 3rd ed.
- Billingsley (1986) Probability and Measure, Wiley Series in
Probability and Mathematical Statistics.
- Shiryayev (1984) Probability, Graduate Texts in Mathematics,
Springer-Verlag.
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Last updated: 30 October 2002.