Lectures

• Philosophical foundations
• Analysis review
• Linear algebra and the multivariate normal distribution
• Convergence
• Characteristic functions
• Lindeberg-Feller CLT
• Transformations
• Exponential families
• Score and information
• Likelihood: Consistency
• Likelihood: Asymptotic normality

• Likelihood: Asymptotic efficiency

• Likelihood: Inference
• Conditional likelihood
• Pseudo-likelihood
• Miscellaneous other results

Occasionally proofs are omitted, although I try to cite a textbook providing the proof when I do so. Three common sources that I cite here are:

• Casella2002: Statistical Inference (2002), Casella and Berger.
• Rudin1976: Principles of Mathematical Analysis, 3rd edition (1976), Rudin.
• Billingsley1995: Probability and Measure, 3rd edition (1995), Billingsley P.

Introduction

To help students get started with the writing of analytic proofs, I wrote this introduction to proofs, which also contains some exercises and solutions.

You may also wish to go over this matrix algebra review.