Face-to-face , first term, 22,5 hours of theory and 22,5 hours of exercises.

First term
Friday from 09:00 to 11:00 at 109 Marais 301

The lecture and the exercise sessions are taught in French. Certain reference books are in English.

As statistical applications are multidimensional in practice, this methodological course is intended to introduce the students to the multivariate aspect of statistics. F. Schaaff's sentence in The Starry Room, illustrates the multidimensional reality of problems submitted to statistics: “The fate of a meteoroid entering earth's atmosphere depends on the mass, velocity, angle of entry, composition, shape, peculiarities of breaking and other factors, all of which are not just variable but also interdependent”. A great number of elements, not just one, determine this random phenomenon as it is described.
At the end of the first 22,5 hours of the course, the students should have been introduced to the concepts of multivariate statistics (they are generally the multidimensional version of fundamental statistical concepts studied in the Probabilities and Extensive Statistics course) but also to their writing using Matrix Calculation. So the complexity of the course lies not only in the use of Matrix Calculation, but also in the use of multidimensional statistical concepts. The data analysing methods initially presented in the first part of the course, will have familiarised the students with the questioning in regards to the actual data which one can dispose of: indispensable preliminary phase for any statistical analysis. The Multivariate Probabilities and Inference sections in this first part of the course will have introduce theoretically the model of linear regression starting from the extensive study of the Multivariate Normal Distribution and its properties.

This first part of the course of Multivariate Statistical Analysis and Econometrics will have prepared students for the second part, the Econometrics part, using these multivariate statistical concepts mainly around the regression model.

For the Bachelor : Business Engineering :

None

In the last few decades, the multivariate statistical methods have become increasingly popular among all kinds of scientists, and particularly among economists. The theory has made tremendous progress; the same thing happened with the applications of the multivariate methods thanks to the development of computer science.

Multivariate Statistical Analysis concerns analysis, in the broadest sense of the term, of data collected in a multidimensional way on a single individual; the aim is not to juxtapose applications used in a one-dimensional case (see Extensive Statistics course) but to consider the joint aspect of the problem. It is this characteristic of interdependence that distinguishes multivariate data and techniques from univariate data and techniques.

1. Multivariate Statistical Analysis: (see syllabus D. Deprins)

- Introduction: Descriptive Techniques
- Part 1: Data Analysis
1) Principal Component Analysis
2) Discriminant Analysis

Reminders of Matrix Calculation, Extensive Statistics and Simultaneous Confidence Intervals (Chapter 1)*

- Part 2: Multivariate Probabilities and Multivariate (Normal) Sampling

3) Samples of a multivariate normal population (Chapter 3)
3.1) Introduction
3.2) Multidimensional Random Variables
3.3) Multivariate Normal and Concentration Ellipsoid
3.4) Theorem of Multivariate Normal with Multiple Regression, Coefficients of Partial and Multiple Correlation
3.5) Multivariate Normal Sampling: Maximum Likelihood and Properties of the Estimators
3.6) and 3.8) Correlation and Multiple Regression

- Part 3: Multivariate Inference

4) Tests on Means (Chapter 4)
4.1) General Results
4.2) Comparisons of Two Means
4.3) Repeated Measures
*The chapter numbers are those of the reference book (Morrison) quoted below in the Bibliography section. Chapter 2 is a reminder of Linear Algebra.

2. Econometrics (see book by Hill R.C., Griffiths W.E. and G.G. Judge (2001) Undergraduate Econometrics)

- Chap 1: An Introduction to Econometrics
- Chap 2: Some Basic Probability Concepts
- Chap 3: The Simple Linear Regression Model: Specification and Estimation
- Chap 4: Properties of the Least Squares Estimators
- Chap 5: Inference in the Simple Regression Model: Interval Estimation, Hypothesis Testing and Prediction
- Chap 6: The Simple Linear Regression Model: Reporting the Results and Choosing the Functional Form
- Chap 7: The Multiple Regression Model
- Chap 8: Further Inference in the Multiple Regression Model
- Chap 9: Dummy (Binary) Variables
- Chap 10: Nonlinear Models
- Chap 11: Heteroskedasticity
- Chap 12: Autocorrelation
- Chap 13: Random Regressors and Moment Based Estimation
- Chap 14: Simultaneous Equations Model

Lecture, exercise sessions, reference books, exercises on real data and computer support.

The lecture is a systematic initiation to the theoretical and methodological foundations of Multivariate Statistical Analysis and Econometrics. Examples illustrate the theory. An effort is made throughout the course to involve the students in the discovery and development of statistical concepts and their applications as well as those linked to econometric problems. This active participation in class should enable the students to fully benefit from the exercise sessions that complete the lecture and to immediately engage in a research approach. However, due to the complexity of the subject matter, the students are invited to read the notes or the chapter relating to the following course beforehand, in order to facilitate an active participation in class.

The course is based on two educational supports available at the reprography service: a syllabus for the Multivariate Statistical Analysis section and a reference book for the Econometrics section (Hill R. C., Griffiths W. E. and G. G. Judge (2001): Undergraduate Econometrics, 2d edition, John Wiley & Sons, Inc.). A website (http://www.wiley.com/college/hill/) is accessible to students, they will find supporting materials such as the data files with exercises and examples from the reference book, SAS files, SHAZAM, EVieuws and EXCELL for the book examples, useful links to other sites etc. Other references that helped construct the lecture can be found under the Bibliography section.

Mister Ayadi supervises the exercise sessions (tutorials); a collection of exercises (in continuous development) is available at the reprography service. Mister Ayadi will help the students to solve most of the exercises and to achieve the piece of work on real data by introducing them to the adapted statistical software available at the Faculties. The practicalities of the work (object, timing, volume, level of requirements, evaluation etc.) will be proposed and discussed during the lecture and the tutorials.

Mister Ayadi will set reception hours, which the students are asked to respect.

The summative evaluation will be a written examination and an oral presentation of the work achieved on real economic data, organised during the exam session. During the oral presentation, teachers are likely to question students on the statistical and econometric theory as well as the practical work carried out during the year.

- Bourbonnais R. (2005) : Econométrie, 6ème édition, Dunod, Paris.
- Greene W., (2005) : Econométrie, 5ème édition (édition française), Pearson Education, Paris.
- Gujarati D. N. (2004), Econométrie, traduction de la 4ème version américaine, Ouvertures Economiques, de Boeck.
- Härdle W. and L. Simar (2003): Applied Multivariate Statistical Analysis, Springer-Verlag.
- Hill R. C. and G. G. Judge (?), Learning and Practicing Econometrics: SAS Handbook, Wiley Edition.
- Hill R. C., Griffiths W. E. and G. G. Judge (2001): Undergraduate Econometrics, 2d edition, John Wiley & Sons, Inc.
- Hill R. C., Griffiths W. E. and G. G. Judge (2001): Using Excel For Undergraduate Econometrics, 2d edition, John Wiley & Sons, Inc.
- Hill R. C., Griffiths W. E. and G. G. Judge (2001): Using EViews For Undergraduate Econometrics, 2d edition, John Wiley & Sons, Inc.
- Mannkiw N. G. (1998): Principes de l'Economie, Economica, Paris.
- Morrison D. F. (2004): Multivariate Statistical Methods, 3th edition, McGraw-Hill Internationnal Editions.
- Stock J. H. and M. W. Watson (2007): Introduction to Econometrics, 2d edition, Pearson International Edition
- Varian H. R. (2002): Introduction à la Microéconomie, 5ème édition (traduction de la 6ème version américaine), Ouvertures Economiques, de Boeck.

- A course syllabus available at the syllabus service for the Multivariate Statistical Analysis section;
- A reference manual for the Econometrics section: Hill R. C., Griffiths W. E. and G. G. Judge (2001) Undergraduate Econometrics, 2d edition, John Wiley & Sons, Inc.
- A collection of exercises for tutorials;
- Notes for the use of the software used for the work on real data.