Basic knowledge of Probabilities. Basic knowledge of mathematical analysis. Mathematical Analysis I and Mathematical Analysis II. Probabilities or Statistical Treatment of Data.
Exposition of concepts and methods based in applied survey problems. Computational tracking when describing the behavior of plans and estimators. Computational implementation of plans and estimators in order to develop critical capacity for practical questions.
Students must understand how to characterize, build and implement a sampling plan. They must learn how to build and optimize estimators. When studying sampling plans, they must understand the limitations and the advantages of each of the plans. They must also be able to plan and execute a sampling or a survey, building the relevant estimators. They will learn how to treat computationally problems with real or simulated data.
Capacity for calculation:
Competence in using computational tools;
Knowledge of mathematical results;
Capacity for generalization and abstraction;
Capacity for formulating and solving problems;
Conception or use of mathematical models in real situations;
Rigorous and clear written and spoken expression;
Capacity for research;
Capacity for autonomous learning;
1. Sampling plans, algorithms of choice, probabilities of inclusion.
2. Inference when sampling, building non-skew estimators, comparing estimators, optimum estimators and allowable estimators.
3. Horvitz-Thompson estimator, properties, allowability and optimality, estimation of variance, non-negativity.
4. Simple random sampling, properties of estimators, characterizations of a sample, composition of plans and building variants.
5. Stratified sampling, properties of estimators, advantages of stratification, optimization of stratum, estimation of precision gains.
6. Sampling by groups in one or two steps, properties of estimators, estimation of variation.
7. Auxiliary measures – IIPS sampling plans, Brewer, Lahiri-Midzuno and Hedayat-Lin algorithms, properties of Horvitz-Thompson estimators in these planes.
Solution of problems – (0 - 40%); Project – (20 - 50%); Mid-term test – (50 - 100%); Exam – (50 - 100%): 100.0%
HEDAYAT, A.S.; SINHA, B.K. (1991). Design and inference in finite population sampling. Wiley.
THOMPSON, S. (2002). Sampling. Wiley.
COCHRAN, W. (1977). Sampling techniques. Wiley.
LOHR, S. (1999). Sampling: design and analysis. Duxbury Press.