The highly readable text captures the flavor of a course in mathematical statistics without imposing too much rigor; students can concentrate on the statistical strategies without getting lost in the theory. Students who use this book will be well on their way to thinking like a statistician. Practicing statisticians will find this book useful in that it is replete with statistical test procedures (both parametric and non-parametric) as well as numerous detailed examples.


Table of contents

I. Regression and Its Generalizations
• Regression Basics
• The Truth about Linear Regression
• Model Evaluation
• Smoothing in Regression
• Simulation
• The Bootstrap
• Splines
• Additive Models
• Testing Regression Specifications
• Weighting and Variance
• Logistic Regression
• Generalized Linear Models and Generalized Additive Models
• Classification and Regression Trees
  II. Distributions and Latent Structure
• Density Estimation
• Relative Distributions and Smooth Tests of Goodness-of-Fit
• Principal Components Analysis
• Factor Models
• Nonlinear Dimensionality Reduction
• Mixture Models
• Graphical Models
  III. Causal Inference
• Graphical Causal Models
• Identifying Causal Effects
• Estimating Causal Effects
• Discovering Causal Structure
  IV. Dependent Data
• Time Series
• Simulation-Based Inference
  Appendices
  
  • Data-Analysis Problem Sets
  • Reminders from Linear Algebra
  • Big O and Little o Notation
  • Taylor Expansions
  • Multivariate Distributions
  • Algebra with Expectations and Variances
  • Propagation of Error, and Standard Errors for Derived Quantities
  • Optimization
  • chi-squared and the Likelihood Ratio Test
  • Rudimentary Graph Theory
  • Writing R Functions
  • Random Variable Generation