Teachings

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Professor
MONICA MUSIO (Tit.)
Period
First Semester
Teaching style
Convenzionale
Lingua Insegnamento
ITALIANO

Informazioni aggiuntive

Course Curriculum CFU Length(h)
[60/64]  MATHEMATICS [64/00 - Ord. 2017]  PERCORSO COMUNE 8 64

Objectives

KNOWLEDGE AND UNDERSTANDING:
Provide basic concepts and tools of statistical methodology needed for each type of statistical analysis, and highlight some theoretical and applicative aspects of the discipline.
APPLYING KNOWLEDGE AND UNDERSTANDING:
Ability to tackle and solve problems and applications of both descriptive and inferential statistics.
MAKING JUDGEMENTS:
The course aims to stimulate the objective evaluation of the teaching by constantly proposing to students a comparison between the theoretical contents proposed during the frontal lessons and their acquisition through the independent study using the suggested texts and the didactic material provided.
COMMUNICATION SKILLS:
The course should provide a minimum basis of descriptive and inferential statistical terminology, which is part of the modern mathematical language.
LEARNING SKILLS:
The course through the holding of a large number of exercises and applications on all topics, tries to teach a general approach to troubleshooting from descriptive and inferential statistics. It is also structured in such a way as to make the study of the student independent. The methods described and treated during the course, are the foundations of all of all the advanced courses in Statistics Methodology. The student should be able to understand more complex statistical methodologies.

Prerequisites

Familiarity with the concepts of analysis in 1 and several variables, elements of linear algebra and analytical geometry. Students must have acquired the knowledge and skills of an introductive course in Probability theory .

Contents

• Elements of descriptive Statistics: statistical distributions, graphical representations, position, dispersion and shape indices. Linear regression and correlation. The concept of mean (following Oscar Chisini).

• Theory of the sample: Population and sample, definition of statistical model, random variables "statistical" sampling distribution and sample moments. Chi-square, Student's t-distribution, F-Snedecor distribution.

• Statistical inference for parametric statistical models: the likelihood function, sufficient statistics, minimal and complete statistics, ancillary statistics, Basu's theorem, ; Fisher information; exponential family; point estimators and their properties; the mean square error, Cramér-Rao inequality (with proof), Rao-Blackwell theorem (with proof), Lehmann-Scheffe theorem (with proof), the method of moments; the method of maximum likelihood and related asymptotic properties; confidence intervals and the method of the variable "pivot"; confidence intervals approximated. Simple and composite hypothesis tests, tests functions, power function, the critical region; Neyman-Pearson theorem (with proof), monotone likelihood ratio families; uniformly most powerful tests, Kurl-Rubin's theorem, the likelihood ratio test.

• Nonparametric methods: chi-square test of fit (with proof); fit testing, Kolmogorov-Smirnov test. Crosstabs. Test of homogeneity. Tests of stochastic independence of two random variables.

• Linear Models: Regression analysis and Gauss-Markov Theorem (with proof). Statistical inference in linear models with normal errors. Goodness of fit of the model. Prediction.

All theoretical arguments will be integrated will practical analysis conducted by means of the statistical package R.

Teaching Methods

Compatibly with the mixed teaching method foreseen in the Manifesto Accademico 2021-22 as a consequence of the COVID-19 emergency, the tools used for the lectures will be both the blackboard and tablet with projection system via classroom screen and via internet streaming. The course includes 32 frontal lectures of 2 hours each, some examples are done with the support of the statistical package R and 16 exercises of 2 hours each. The latter are assisted by an expert tutor.
For the preparation of the student at home there is a website (https://www.unica.it/unica/it/ateneo_s07_ss01.page?contentId=SHD30604) where students can find instructor's notes, weekly exercises to perform at home (corrected in class by a tutor) and tests of previous examinations.

Verification of learning

Compatibly with the indications of the University on how to carry out the exams according to the evolution of the COVID-19 emergency, the exams could be held in the presence or online.
Examination consists of a written test and an oral exam.
The written test consists in a selection of 4 or 5 exercises similar to those assigned in the tutorial. Students have 2 hours and half for the written test. In particular will be evaluated the problem solving ability as well as the appropriate use of tools from statistics.
Students who pass the written test are admitted to the oral test. The oral test is passed if the student responds correctly to at least three questions on various topics of the course program. In any case an excessively insufficient response may compromise the whole oral examination.
The oral exam consists of a discussion on topics covered by the lectures. The student must demonstrate that they have understood and assimilated the arguments put forward during the lessons. In addition, students must demonstrate that they are able to explain the concepts and demonstrations learned during the course. If a student fails to get a positive result during the second half of the exam he must apply again for the first part. Students must also be able to carry out simple exercises of statistical analysis using the statistical package R.

The final grade is a weighted average of both tests.

Texts

Textbook
P.Baldi Introduzione alla Probabilità con elementi di statistica (1 capitolo)(2003), McGraw Hill
- G.Casella, R.L.Berger (2001), Statistical Inference, Duxubury Press.
Other books
- M.Mood, F.Graybill, D.Boes (1974), Introduction to the Theory of Statistics, McGraw-Hill.
- G.J.Kerns (2011) Introduction to Probability and Statistics Using R (https://cran.r-project.org/web/packages/IPSUR/vignettes/IPSUR.pdf).