### Teachings

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

Informazioni aggiuntive

Course Curriculum CFU Length(h)
[60/64]  MATHEMATICS [64/00 - Ord. 2012]  PERCORSO COMUNE 7 56

### 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 [6 hours]: statistical distributions, graphical representations, position, dispersion and shape indices. Linear regression and correlation. The concept of mean

• Theory of the sample [8 hours]: 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 [20 hours]: the likelihood function, sufficient statistics, complete; Fisher information; exponential family; point estimators and their properties Cramér-Rao inequality, Rao-Blackwell theorem, Lehmann-Scheffe theorem, 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, monotone likelihood ratio families; uniformly most powerful tests, likelihood ratio test.

• Nonparametric methods [10 hours]: chi-square test of fit; fit testing, Kolmogorov-Smirnov test. Crosstabs. Test of homogeneity. Tests of stochastic independence of two random variables.

• Linear Models [12 hours]: Regression analysis and Gauss-Markov Theorem. Statistical inference in linear models with normal errors. Goodness of fit of the model. One-way analysis of variance. Multiple comparisons and the Bonferroni method.

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

### Teaching Methods

Traditional teaching on blackboard (56 hours), exercises theoretical and practical using the statistical package R (28 ore).
During the course, will be proposed some practical exercises to do at home using the statistical package R. These exercises must be delivered to the teacher and will be taken into account for the final evaluation.

### Verification of learning

Written and oral test. The written test consists in a selection of 3 or 4 exercises similar to those assigned in the tutorial. Students have 2 hours and half for the written test. The oral test is passed if the student responds correctly to at least three questions on various topics of the course program.
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. In any case an excessively insufficient response may compromise the whole oral examination. The final grade is determined by the vote of both the tests and the proper conduct of the practical exercises assigned during the course.

### 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).