Statistical Theory: A Concise Introduction

Introduction
Preamble
Likelihood
Sufficiency
Minimal sufficiency
Completeness
Exponential family of distributions


Point Estimation
Introduction
Maximum likelihood estimation
Method of moments
Method of least squares
Goodness-of-estimation. Mean squared error.
Unbiased estimation


Confidence Intervals, Bounds, and Regions
Introduction
Quoting the estimation error
Confidence intervals
Confidence bounds
Confidence regions


Hypothesis Testing
Introduction
Simple hypotheses
Composite hypotheses
Hypothesis testing and confidence intervals
Sequential testing


Asymptotic Analysis
Introduction
Convergence and consistency in MSE
Convergence and consistency in probability
Convergence in distribution
The central limit theorem
Asymptotically normal consistency
Asymptotic confidence intervals
Asymptotic normality of the MLE
Multiparameter case
Asymptotic distribution of the GLRT. Wilks’ theorem.