ENSAE Paris - École d'ingénieurs pour l'économie, la data science, la finance et l'actuariat



The objective of the course is to present:

  • the inference principles in finite population sampling theory,
  • the most common sampling methods,
  • the reweighting methods (calibration, or adjustment for non-response).

Main learning outcomes: at the end of the course, the student will know how to:

- Define a sampling design adapted to the problem posed, in the case of simple surveys,
- Calculate estimators and their precision,
- Correct a survey for unit or item non-response.

Assessment method:

Written exam (100%).


  1. Finite population sampling. Sampling design, measures of accuracy, inclusion probabilities, Horvitz-Thompson estimation, choice of inclusion probabilities, confidence intervals, case of a function of totals.
  2. Simple random sampling. Estimating a mean, a total, a proportion. Calculation and estimation of precision. Determining the sample size. Sampling algorithms.
  3. Stratification. Principle. Estimation and estimation of precision. Sample allocation between strata. Constitution of strata.
  4. Unequal probability sampling. Sampling algorithms: Poisson sampling, systematic sampling, pivotal method, Chao's method.
  5. Multistage sampling. Cluster sampling: estimating a total, precision. Two-stage sampling: estimating a total, precision. Case of a simple random sample at each stage. Self-weighting sample surveys.
  6. Reweighting methods. Principles, calibration method and its applications: regression estimation, ratio estimation, post-stratification estimation.
  7. Correcting non-response. Type of non-response. Reweighting for unit non-response. Imputation for item non-response.



  • Ardilly P. (2006). Les techniques de sondage. Technip, Paris.
  • Sarndal C.E., Swenson B., Wretman J. (2003). Model assisted survey sampling. Springer, New-York.
  • Tillé Y. (2020). Sampling and estimation from finite populations. Wiley, New-York.