Robust statistical inference · location and scale estimation

Introduction

What this guide covers

Classical statistical inference is grounded in highly restrictive distributional assumptions, with the normal distribution acting as the fundamental mathematical pillar of most optimal methods. However, in empirical practice, departures from normality—such as heavy tails, latent asymmetries, and the presence of outliers or contaminants—are common.

Overview

Topics covered

• Introduction
• Robust Statistics: Location and Scale Estimation
• Historical perspective and crisis of the classic paradigm of normality
• Theoretical foundations: concept of robustness and sensitivity measures
• 1. Qualitative Robustness
• 2. Breakdown Point

Related concepts

Main connections

• Median & robust location
• Mean & expected value
• Variance & standard deviation
• Calculus & differentiation
• Residual analysis & diagnostics
• Linear regression

Compatible notation

Mathematical sample in LaTeX

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