Sampling Theory

Objectifs

At the end of this course, students should know and master the main sampling methods used in the case of a finite population (stratification, unequal probability sampling, cluster sampling), as well as the properties of the associated estimators (Horvitz-Thompson estimator, substitution estimator). Part of the course is also devoted to the presentation of adjustment methods, in which external information is used to modify estimators in order to reduce their variance. The notion of a working model should also be mastered by the end of the course

Plan

Part 1: Sampling in finite populations
Notations
Sample design, Horvitz-Thompson estimation
Precision calculation: variance estimator, confidence interval.

Part 2: Sampling methods
Simple random sampling
Stratified simple random sampling
Unequal probability sampling
Cluster sampling

Part 3: Estimation methods
Model-assisted approach
Calibration estimator
Applications: regression estimator, ration estimator, post-stratified estimator

Part 4: Additional information on sampling methods
Balanced sampling
Sample coordination

Part 5: Additional information on estimation methods
Estimation of a totals function
Treatment of nonresponse

Prérequis

Probability, Complements to probability, Descriptive statistics and SAS, Statistics with R