Probability & Statistical Inference · Statistical Inference & Estimation

Estimation methods — Statistical inference

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction 𝔼[T] Statistical Inference Unit II · Estimation Theory

Overview

Topics covered

  • Introduction
  • Estimation Methods
  • Introduction to Estimation
  • Types of Estimation
  • General Framework: Loss Function
  • Properties of Estimators

Related concepts

Main connections

  • Maximum likelihood estimation
  • Bayes' theorem & priors
  • Bootstrap resampling
  • Variance & standard deviation
  • Quantiles & percentiles
  • Mean & expected value

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

R(θ,T)=𝔼θ[L(θ,T(𝐗))]=∫𝒳nL(θ,T(𝐱))dPθn(𝐱)
View LaTeX sourceR(\theta, T) = \mathbb{E}_\theta\!\left[L\!\left(\theta,\, T(\mathbf{X})\right)\right] = \int_{\mathcal{X}^n} L\!\left(\theta, T(\mathbf{x})\right)\, dP_\theta^n(\mathbf{x})