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STAT 3559

Mathematical Statistics (Honours)

0.5 credit · Undergraduate

Empirical distribution functions, Monte Carlo methods, elements of decision theory, point estimation, interval estimation, tests of hypotheses, robustness, nonparametric methods.

2021

Topics

  • Parametric statistical models. Concept of an estimator. Basic criteria 7.1, 8.7
  • Consistency and unbiasedness of the sample mean and the sample 8.7 (Cont)
  • Fisher’s lemma. Confidence intervals: general definition; confidence 8.3, 8.5
  • Gamma distribution: definition and properties. Beta distribution: 5.7, 5.8
  • Notions of statistical model, parameter space, loss function, and 7.4
  • Sufficient statistics: definition, Neyman-Fisher factorization theorem, 7.7-7.9
  • Method of moments. Regular families of distributions. Fisher 8.8
  • Method of maximum likelihood: definition of a MLE, invariance 7.5, 8.8
  • Basic concepts of the Neyman-Pearson approach to hypothesis 9.1
  • Most powerful tests. Families of distributions with a monotone 9.2-9.3
  • Chi-square test of goodness-of-fit for a simple hypothesis. Chi- 10.1-10.4
  • Kolmogorov-Smirnov one-sample tests of goodness-of-fit. 10.6, 10.8

Prerequisites & course information

Precludes additional credit for STAT 3509 , STAT 4321 . Prerequisite(s): STAT 3558 with a grade of C- or higher; or ( STAT 3508 with a grade of B or higher, and permission of the instructor); or permission of the School. Lectures three hours a week, tutorial one hour a week.

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