Statistics 375
Mathematical Statistics
Textbook
Mathematical Statistics and Data Analysis, 3/e
,
by John Rice, Cengage Learning, 2007
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.
2. Random Variables
Discrete Random Variables
Continuous Random Variables
Functions of a Random Variable
3. Joint Distributions
Discrete Random Variables
Continuous Random Variables
Independent Random Variables
Conditional Distributions
Functions of Jointly Distributed Random Variables
Extrema and Order Statistics
4. Expected Values
The Expected Value of a Random Variable
Variance and Standard Deviation
Covariance and Correlation
Conditional Expectation and Prediction
The Moment-Generating Function
Approximate Methods
5. Limit Theorems
The Law of Large Numbers
Convergence in Distribution and the Central Limit Theorem
6. Distributions Derived from the Normal Distribution
Chi-Squared, t, and F Distributions
The Sample Mean and Sample Variance
7. Survey Sampling
Population Parameters
Simple Random Sampling
Estimation of a Ratio
Stratified Random Sampling
Surveys (
zip
html
)
8. Estimation of Parameters and Fitting of Probability Distributions
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
)
9. Testing Hypotheses and Assessing Goodness of Fit
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
)
10. Summarizing Data
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
)
11. Comparing Two Samples
Comparing Two Independent Samples
Comparing Paired Samples
Experimental Design
Two Samples (
zip
html
)
12. The Analysis of Variance
The One-Way Layout
The Two-Way Layout
ANOVA (
zip
html
)
13. The Analysis of Categorical Data
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
)
14. Linear Least Squares
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
)
Resources
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
cparrish@sewanee.edu