Statistical Modeling & Regression · Non-Parametric Statistics

Advanced nonparametric statistics · Advanced biostatistics

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Expert Level Treatise

Overview

Topics covered

  • Introduction
  • Advanced Nonparametric Statistics: Beyond Ranges
  • General Theory of U-Statistics and the Projection Method
  • 1.1 Formal Definition of Estimable and U-Statistical Functionals
  • 1.2 The Hoeffding Decomposition (Hájek Projection)
  • Empirical Processes, Empirical CDF and Donsker's Theorem

Related concepts

Main connections

  • Calculus & differentiation
  • Variance & standard deviation
  • Linear algebra & matrices
  • Bootstrap resampling
  • Non-parametric tests
  • Linear regression

Compatible notation

Mathematical sample in LaTeX

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

𝔼F[h(X1,…,Xm)]=∫…∫h(x1,…,xm)dF(x1)…dF(xm)=θ(F)∀F∈ℱ
View LaTeX source\mathbb{E}_F[h(X_1, \dots, X_m)] = \int \dots \int h(x_1, \dots, x_m) \, dF(x_1) \dots dF(x_m) = \theta(F) \quad \forall F \in \mathcal{F}