Statistical Methods and Applications

PIER LUIGI CONTI
PIER LUIGI CONTI

Learning goals
The primary goal of the course on “Sample Surveys” is that student should learn the main problems and methods in sampling from finite populations. They should be able to formalize and plan the whole process of data collection and analysis in observational studies.
In more detail, students should be able to plan a sample survey, to choose a sampling design, to plan the data collection, as well as to analyze real data and to estimate quantities of interest.

Knowledge and understanding
After attending the course the students know and understand the main methodologies in planning a sample survey, as well as in dealing with non-sampling sources of error, such as nonresponses and missing values, measurement errors, list imperfections. Furthermore, students should be able to analyze real data and to estimate quantities of interests, such as means and proportions.

Applying knowledge and understanding
At the end of the course the students are able to formalize and plan the whole process of data collection and analysis in observational studies. They should be able to manage the most important (i) sampling designs and (ii) point and interval estimators, as well as the main methodologies to deal with missing values, measurement errors, list imperfections. Moreover, they should be able to apply the methods to the data and to interpret the results.

Making judgements
Students develop critical skills through the application of sampling and estimation methodologies to a wide range of contexts.
They also develop the critical sense through the comparison of different solutions and the analysis of results.

Communication skills
Students, through their study, should acquire the technical-scientific language of the discipline, to be used in their activity.

Learning skills
Students who pass the exam have learned a method of analysis to be used in the data collection and analysis from finite populations."

An elementary course in "Statistical Inference" + an elementary course in "Sampling Techniques"

- Basic aspects on variable probability sampling designs
- Inclusion probabilities: properties and approximations
- Some relevant examples: simple random sampling, stratified random sampling, single-stage cluster sampling, two-stage sampling, systematic sampling, ppswr, ppswor, Midzuno-Lahiri sampling design
- Theory of statistical inference in random sampling under fixed-population approach: "flat" likelihood.
- Horvitz-Thompson estimator and its properties. The problem of variance estimation: exact and approximate solutions.
- Sampling designs with pre-fixed inclusion probabilities: Poisson, Bernoulli, Pareto, Sampford, Conditional Poisson, sampling designs.
- Balanced sampling designs and cube sampling algorithm
- Calibration estimators, with applications to post-stratification and estimation in contingency tables. IPF algorithm.
- Variance estimation by linearization technique.
- Resampling based on pseudo-populations: general aspects and applications to variance estimation.
- Non-sampling errors: general aspects
- Frame imperfections. Dual frame sampling.
- Measurement errors models. Effects of measurement errors.
- Non-responses: general aspects. Methodologies to prevent non-responses. Methodologies to data weight.
- Nonrespondents sampling: the Hansen-Hurwitz approach in a modern perspective.
- Randomized response techniques
- Estimation of response probabilities via homogeneous response groups
- Superpopulation models: basic aspects
- Design-based, model-based, model-assisted approaches to inference for superpopulation parameters
- Ignorability of sampling designs and consequences of non-ignorability: the emerging of model-assisted inference.
- Weighted log-likelihood
- Regression analysis for survey data. GREG estimator
Statistical inference in contingency tables for survey data.

Lectures notes

Classroom lectures

The course consists of 72 hours (9 credits)
Lectures are held in classroom, in traditional mode.

Written or oral examination + optional project.