33400 - Sampling Methods and Data Analysis

Learning outcomes

By the end of the course the student gains an appreciation of the types of problems and questions which arise with multivariate data and the basic theory of survey sampling.
In particular the student should be able:- to apply and interpret methods of dimension reduction (including principal component analysis and factor analysis); - to apply and interpret methods for cluster analysis and discrimination; - to interpret the output of R procedures for multivariate statistics - to employ simple, stratified and probability sampling; - to derive the estimators and associated standard errors of population in the different sampling strategies; - to correct estimation by the ratio principle; - to understand the difference between observational and experimental studies.

Course contents

Module 1: Survey Sampling

Inference in finite and infinite populations.
Inference based on sampling design.
Simple random sampling with and without replacement.
Sampling with varying probability: the Horvitz Thompson and Hansen Hurwitz estimators.
The use of auxiliary information: ration and regression estimators.
Stratification and clustering.

Module 2: Data Analysis

Principal component analysis - Geometrical concepts. Mathematical details. Properties and practical considerations. Principal component analysis in regression.

Factor analysis - The linear factor model: specification, identification, estimation.

Cluster analysis - Distances and dissimilarities. Hierarchical clustering methods. K-means clustering.

Discriminant analysis - Discrimination when the populations are known (maximum likelihood and bayes discriminant rules). Discrimination under estimation. Fisher's linear discriminant function. Probabilities of misclassification.

Module 3: Topics in Linear Algebra

Real quadratic rorms and real symmetric matrices – Classification methods. Sylvester ‘s law of inertia. Rayleigh quotient.

Singular value decomposition (SVD) of a real matrix – Algebraic and statistical properties and applications of SVD.

Readings/Bibliography

Module 1: Survey Sampling

Downloadable lecture notes: Daniela Cocchi "Teoria dei Campioni (corso base)"

Sharon Lohr, “Sampling: design and analysis”, Pacific Grove, Duxbury press, 1999.

Some additional readings will be indicated during the course.

Module 2: Data Analysis

S. Mignani, A. Montanari, Appunti di analisi statistica multivariata, Esculapio, Bologna, 1994.

W.J. Krzanowski, Principles of Multivariate Analysis: A User's Perspective, 1988, Oxford University Press.

Module 3: Topics in Linear Algebra

Downloadable lectures notes from AMS Campus

C.D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM, 2000.

Teaching methods

Module 1: Survey Sampling

Lectures

Module 2: Data Analysis

Lectures and practicals

Module 3: Topics in Linear Algebra

Lectures

Assessment methods

The assessment aims to evaluate the achievement of the following learning objectives:

• knowledge of the fundamental aspects of sampling from finite populations
• proper use of the statistical tools for design sampling plans

• knowledge of the multivariate analysis methods explained in the lectures

• proper use of the explained multivariate methods to the analysis of data matrix

The exam is written and oral and the evaluation is expressed as a grade of out of 30.

The evaluation of the course "Survey Sampling and Data Analysis" is the average of the evaluations of the two units. The knowledge of topics in Linear Algebra is checked during the oral exam of Data Analysis.

Teaching tools

Slides.

Links to further information

http://www.unibo.it/docenti/michele.scagliarini

Office hours

See the website of Michele Scagliarini

See the website of Angela Montanari

See the website of Laura Guidotti