STATS 426 - Introduction to Theoretical Statistics
Section: 002
Term: FA 2009
Subject: Statistics (STATS)
Department: LSA Statistics
Requirements & Distribution:
Waitlist Capacity:
Advisory Prerequisites:
STATS 425.
This course counts toward the 60 credits of math/science required for a Bachelor of Science degree.
May not be repeated for credit.
Primary Instructor:

This course covers the basic ideas of statistical inference, including sampling distributions, estimation, confidence intervals, hypothesis testing, regression, analysis of variance, nonparametric testing, and Bayesian inference. The sequence of STATS 425/426 serves as a prerequisite for more advanced Statistics courses. Regular homework and a final exam.

Topic covered include:

  • Random Variables
  • Joint Distributions
  • Induced Distributions
  • Expectation
  • The Law of Large Numbers
  • The Central Limit Theorem
  • Simulation
  • Populations and Samples
  • The Chi-squared, t, and F Distributions
  • Estimation: The Method of Moments
  • Maximum Likelihood Estimation
  • Bias, Variance, and MSE
  • The Cramer Rao Inequality
  • Exponential Families and Sufficiency
  • Confidence Intervals
  • Approximate Confidence Intervals
  • The Bootstrap
  • Asymptotics of the MLE
  • Tests and Confidence Intervals
  • Neyman Pearson
  • Likelihood Ratio Tests
  • Chi-Squared Tests
  • Goodness of Fit Tests
  • The Sample Distribution Function
  • Decision Analysis
  • Bayesian Inference
  • The Two Sample Problem
  • More on the Two Sample Problem
  • Rank Tests
  • One Way ANOVA
  • Simultaneous Confidence
  • Two Way ANOVA
  • Categorical Data
  • Simple Linear Regression
  • Multiple Regression

STATS 426 - Introduction to Theoretical Statistics
Schedule Listing
001 (LEC)
16STATS (Maj or Min)
MW 4:00PM - 5:30PM
002 (LEC)
10STATS (Maj or Min)
TuTh 2:30PM - 4:00PM
NOTE: Data maintained by department in Wolverine Access. If no textbooks are listed below, check with the department.

Mathematical Statistics and Data Analysis (with CD Data Sets); Author: John A. Rice; 3rd Edition; ISBN 0 534 39942 8 (Student Edition); Duxbury Advanced Series
Syllabi are available to current LSA students. IMPORTANT: These syllabi are provided to give students a general idea about the courses, as offered by LSA departments and programs in prior academic terms. The syllabi do not necessarily reflect the assignments, sequence of course materials, and/or course expectations that the faculty and departments/programs have for these same courses in the current and/or future terms.

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