Eikosstatistics & data science

Experimental Design & Data Collection · Survey Sampling & Estimation

Sampling theory: introduction and mathematical foundations

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Introduction Sampling Theory · Inference in finite populations

Overview

Topics covered

  • Introduction
  • Sampling theory: Mathematical foundations
  • Philosophy of inference in finite population and probability framework
  • Statistical properties of the estimators and decomposition of the MSE
  • Simple Random Sampling (MAS): With and without replacement
  • 3.1 · Simple Random Sampling without Replacement (MASsin / SRSWOR)

Related concepts

Main connections

  • Variance & standard deviation
  • Mean & expected value
  • Unsupervised learning & clustering
  • Survey sampling methods
  • Linear regression
  • Missing data & multiple imputation

Compatible notation

Mathematical sample in LaTeX

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

p(s)≥0∀s∈Ω,∑s∈Ωp(s)=1
View LaTeX sourcep(s) \ge 0 \quad \forall s \in \Omega, \qquad \sum_{s \in \Omega} p(s) = 1