Math 334 & Stat 434 at Lehigh University

Math 334/Stat 434 (Mathematical Statistics): Popolations and random sampling; sampling distributions; theory of estimation; criteria and methods of point and interval estimation; theory of testing statistical hypotheses. Prerequisite: Math 231 or Math 309.

Here is a typical course description of Mathematical Statistics at lehigh University.

Text for the Fall of 2001:  Statistics: Theory & Methods, 2nd edition, by Berry and Lindgren.

Texts used in previous years:
   1. "Mathematical Statistics and Data Analysis", 2nd edition, by John A. Rice.
   2. "Probability & Statistical Inference", by Hogg and Tenis
   3. "Statistical Inference", by Casella and Burger
   4. "Theoretical Statistics", by Cox and Hinkley

Selected topics :

  • Review (sample space, probability measure, conditional probability, independence, randon variables, some known discrete and continuous distributions, joint distributions, expected values, variance, covariance).
  • Moments and Moment generating function.
  • Can moments always uniquely determine a probability distributions?
  • Approximate methods (delta-method and the continuous mapping theorem).
  • Limit theorems (Convergence in probability, LLN, Central Limit Theorem, and convergence in distribution).
  • Distribution derived from normal distribution (Chi-squared, t, F, and other related distributions).
  • Fitting the distribution (minimum chi-squared and other methods).
  • Unbiased and consistent estimator.
  • Method of moments, consistency of moment estimator.
  • Fisher Information and Cramer-Rao Inequality.
  • Exact vs Asymptotic variance, delta-method revisit.
  • Method of maximum Likelihood, large sample thoery for MLE.
  • Empirical Fisher information and approximate confidence interval based on MLE.
  • Regular (smooth) probability family.
  • Sufficient statistics and factorization theorem.
  • Sufficiency and Rao-Blackwell Theorem.
  • MVUE (Minimum Variance Unbiased Estimator).
  • Complete statistics and Lehmann-Scheffe Theorem.
  • Exponential probability family.
  • Order statistics.
  • Hypotheses testing.
  • Probabilities of Type-I and Type-II errors; Power function.
  • N-P Lemma.
  • Likelihood ratio tests.
  • Others

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