Statistics 375 Mathematical Statistics

Textbook

Course Notes

The following outline is from Rice's table of contents.


1. Probability

• Sample Spaces
• Probability Measures
• Computing Probabilities: Counting Methods
• Conditional Probability
• Independence.

• Discrete Random Variables
• Continuous Random Variables
• Functions of a Random Variable

• Discrete Random Variables
• Continuous Random Variables
• Independent Random Variables
• Conditional Distributions
• Functions of Jointly Distributed Random Variables
• Extrema and Order Statistics

• The Expected Value of a Random Variable
• Variance and Standard Deviation
• Covariance and Correlation
• Conditional Expectation and Prediction
• The Moment-Generating Function
• Approximate Methods

• The Law of Large Numbers
• Convergence in Distribution and the Central Limit Theorem

• Chi-Squared, t, and F Distributions
• The Sample Mean and Sample Variance

• Population Parameters
• Simple Random Sampling
• Estimation of a Ratio
• Stratified Random Sampling

• Surveys (zip html)

• Fitting the Poisson Distribution to the Emissions of Alpha Particles
• Parameter Estimation
• The Method of Moments
• The Method of Maximum Likelihood
• The Bayesian Approach to Parameter Estimation
• Efficiency and the Cramer-Rao Lower Bound
• Sufficiency

• Estimation (zip html)

• The Neyman-Pearson Paradigm
• The Duality of Confidence Intervals and Hypothesis Tests
• Generalized Likelihood Ratio Tests
• Likelihood Ratio Tests for the Multinomial Distribution
• The Poisson Dispersion Test
• Hanging Rootograms
• Probability Plots
• Tests for Normality

• Hypothesis Testing (zip html)

• Methods Based on the Cumulative Distribution Function
• Histograms, Density Curves, and Stem-and-Leaf Plots
• Measures of Location
• Measures of Dispersion
• Boxplots
• Exploring Relationships with Scatterplots

• Summarizing Data (zip html)

• Comparing Two Independent Samples
• Comparing Paired Samples
• Experimental Design

• Two Samples (zip html)

• The One-Way Layout
• The Two-Way Layout

• ANOVA (zip html)

• Fisher's Exact Test
• The Chi-Square Test of Homogeneity
• The Chi-Square Test of Independence
• Matched-Pairs Designs
• Odds Ratios

• Categorical Data (zip html)

• Simple Linear Regression.
• The Matrix Approach to Linear Least Squares
• Statistical Properties of Least Squares Estimates
• Multiple Linear Regression — An Example
• Conditional Inference, Unconditional Inference, and the Bootstrap
• Local Linear Smoothing

• Regression (zip html)

• John Rice, UC Berkeley
  
• UCB Statistics 135, Concepts of Statistics, John Rice, F2008, UC Berkeley
  
• UCB Statistics 230A, Linear Models, John Rice, F2006, UC Berkeley
  
• Stanford Statistics 200, Introduction to Statistical Inference, Zhou Fan, F2016, Stanford
  
• Yale Stat 242-542, Theory of Statistics, Andrew Barron, F1999, Yale
  
• MIT 18.650, Statistics for Applications, Philippe Rigollet, F2016, MIT OpenCourseWare
  
• MIT 18.650, Statistics for Applications, Peter Kempthorne, FS2015, MIT OpenCourseWare
  
• MIT 18.650, Statistics for Applications, Dmitry Panchenko, F2006, MIT OpenCourseWare
  
• MIT 18.175, Theory of Probability, Scott Sheffield, F2016, MIT
  
• MIT 18.175, Theory of Probability, Scott Sheffield, F2014, MIT OpenCourseWare
  
• MIT 18.175, Theory of Probability, Scott Sheffield, F2012, MIT
  
• MIT 18.440, Probability and Random Variables, Scott Sheffield, F2014, MIT OpenCourseWare
  
• MIT 18.440, Probability and Random Variables, Scott Sheffield, F2012, MIT
  
• Grinstead and Snell, Introduction to Probability, AMS
  excellent (and free) probability textbook published by the American Mathematical Society, 2/e, 1997
• Grinstead and Snell, Introduction to Probability, website
  supporting website for Grinstead and Snell, Introduction to Probability
• Grinstead and Snell, Introduction to Probability, answers
  answers to odd-numbered exercises in Grinstead and Snell, Introduction to Probability
• Rice Statistics 310, Probability and Statistics, Keith Baggerly, S2002, Rice