Math 334 & Stat 434 at Lehigh University
Math 334/Stat 434 (Mathematical Statistics): Popolations and random
sampling; sampling distributions; theory of estimation; criteria and
of point and interval estimation; theory of testing statistical
Prerequisite: Math 231 or Math 309.
Here is a typical course description of Mathematical Statistics at
Text for the Fall of 2001: Statistics: Theory & Methods,
edition, by Berry and Lindgren.
Texts used in previous years:
1. "Mathematical Statistics and Data Analysis", 2nd
by John A. Rice.
2. "Probability & Statistical Inference", by Hogg
3. "Statistical Inference", by Casella and Burger
4. "Theoretical Statistics", by Cox and Hinkley
Selected topics :
Review (sample space, probability measure, conditional probability,
randon variables, some known discrete and continuous distributions,
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
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
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.
Probabilities of Type-I and Type-II errors; Power function.
Likelihood ratio tests.
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