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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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