Nonparametric statistics: Density estimation · Introduction

Introduction

What this guide covers

A rigorous treatment of the theory underlying the estimation of the probability density function without a priori distributional assumptions. Asymptotic analysis, minimization of the integrated mean square error (AMISE) and optimal selection of the smoothing parameter.

Overview

Topics covered

Introduction
Non-Parametric Density Estimation
Motivation, Context and Theoretical Foundations
The Histogram as a Density Estimator
Exact Statistical Properties of the Histogram
Asymptotic Behavior and the MISE

Related concepts

Main connections

Compatible notation

Mathematical sample in LaTeX

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

P(X \in A) = \int_A f(x) dx \quad \text{for cualquier conjunto of Borel } A \in \mathcal{B}(\mathbb{R}^d)

View LaTeX source

P(X \in A) = \int_A f(x) dx \quad \text{for cualquier conjunto of Borel } A \in \mathcal{B}(\mathbb{R}^d)