Training and Research
PhD Programme Courses/classes - 2023/2024
Mathematical Statistics
Credits: 5
Language: English
Teacher: Catia Scricciolo
Microeconomics 1
Credits: 7,5
Language: English
Teacher: Simona Fiore, Claudio Zoli, Martina Menon
Continuous Time Econometrics
Credits: 5
Language: English
Teacher: Cecilia Mancini
Probability
Credits: 7,5
Language: English
Teacher: Marco Minozzo
Macroeconomics I
Credits: 7,5
Language: English
Teacher: Tamara Fioroni, Alessia Campolmi
Game Theory
Credits: 5
Language: English
Teacher: Francesco De Sinopoli
Mathematics
Credits: 4,5
Language: English
Teacher: Andrea Mazzon, Jonathan Yick Yeung Tam
Advice to Young Economists
Credits: 4
Language: English
Teacher: Marco Piovesan
Stochastic Optimization and Control
Credits: 5
Language: English
Teacher: Athena Picarelli
Financial Time Series
Credits: 5
Language: English
Teacher: Giuseppe Buccheri, Francesca Rossi
Mean Field Games (part I)
Credits: 2,5
Language: English
Teacher: Luciano Campi
Job Market Orientation
Credits: 1
Language: English
Teacher: Joan Madia, Simone Quercia
Discretization of Processes
Credits: 4,5
Language: English
Teacher: Jean Jacod
Topics in applied economics with administrative data
Credits: 1
Language: English
Teacher: Edoardo Di Porto
Multivariate Analysis with Latent Variables: The SEM Approach
Credits: 3
Language: English
Teacher: Albert Satorra
Financial Mathematics
Credits: 5
Language: English
Teacher: Alessandro Gnoatto
Political Economy
Credits: 4
Language: English
Teacher: Emanuele Bracco, Roberto Ricciuti
Finite Mixture Models in Health Economics: Theory and Applications
Credits: 1
Language: English
Teacher: Paolo Li Donni
Inequality
Credits: 4
Language: English
Teacher: Francesco Andreoli, Claudio Zoli
Behavioral and Experimental Economics
Credits: 4
Language: English
Teacher: Simone Quercia, Maria Vittoria Levati, Marco Piovesan
Health Economics
Credits: 4
Language: English
Teacher: Paolo Pertile, Catia Nicodemo
Development economics
Credits: 4
Language: English
Teacher: Federico Perali
Finance
Credits: 4
Language: English
Teacher: Giorgio Vocalelli
Mean Field Games (part II)
Credits: 2,5
Language: English
Teacher: Giulia Liveri
Stochastic Processes in Finance
Credits: 5
Language: English
Teacher: Sara Svaluto Ferro, Christa Cuchiero
Dynamic Corporate Finance
Credits: 2
Language: Englìsh
Mathematical Statistics (2023/2024)
Teacher
Referent
Credits
5
Language
English
Class attendance
Free Choice
Location
VERONA
Learning objectives
Introduce students to the theory of nonparametric estimation through models and examples.
Prerequisites and basic notions
Knowledge of measure theory and probability is assumed.
Program
Introduction to the problem of nonparametric estimation and overview of the course topics:
a. methods of construction of estimators,
b. statistical properties of estimators (convergence and rates of convergence),
c. study of optimality of estimators.
Examples of nonparametric problems and models:
- estimation of a probability density,
- nonparametric regression,
- Gaussian white noise model.
Distances/divergences between probability measures:
- Hellinger and total variation distances,
- Scheffè’s theorem and Le Cam’s inequalities,
- Kullback-Leibler and χ2-divergences,
- link inequalities among distances and divergences.
Estimation of the distribution function: definition of the empirical distribution function and consistency.
Estimation of a probability density:
- definition of the Parzen–Rosenblatt kernel density estimator in the uni- and multidimensional cases, examples of kernels,
- definition of the mean squared error (MSE) of kernel estimators at a point and decomposition into the sum of the variance and the squared bias,
- upper bound on the point-wise variance,
- upper bound on the point-wise bias under regularity conditions on the density and the kernel: definitions of Hölder classes and higher order kernels,
- upper bound on the supremum point-wise MSE of kernel estimators,
- mean integrated squared error (MISE): decomposition into the
sum of the integrated variance and the squared bias,
- control of the variance term,
- control of the bias term on Nikol’ski and Sobolev classes of regular densities, upper bound on the MISE for densities in
Sobolev classes.
Fourier analysis of kernel density estimators:
- preliminary facts on Fourier transforms (FT’s),
- the empirical characteristic function: unbiasedness of the FT for the distribution function, expression of the variance,
- expression of the exact MISE of kernel density estimators,
- control of the bias term over Sobolev classes of densities,
- discussion of the local condition around zero on the FT of the
kernel.
Nonparametric regression:
- nonparametric regression with fixed or random design,
- nonparametric regression with random design and the Nadaraya-Watson (N-W) estimator,
- derivation of the expression of the N-W estimator from kernel
density estimators,
- the N-W estimator as a linear nonparametric regression
estimator,
- asymptotic analysis of the N-W estimator,
- nonparametric regression with fixed (regular) design,
- definition of projection (or orthogonal series) estimators,
- the trigonometric basis as an example of orthonormal basis,
- Sobolev classes and ellipsoids,
- bias and MSE of the coefficient estimators,
- control of the residuals by the condition that the vector of
coefficients belongs to a Sobolev ellipsoid, decomposition of
the MISE of the projection estimator and optimal choice of the
cut-off point,
- upper bound on the MISE for the projection estimator,
- connection between the Gaussian white noise model and
nonparametric regression.
Lower bounds on the minimax risk:
- minimax risk associated with a statistical model and a semi-metric,
- definition of an optimal rate of convergence,
- a general reduction scheme for proving lower bounds,
- main theorem on lower bounds based on many hypotheses using the Kullback-Leibler divergence,
- example of lower bound on the minimax L2-risk for the Hölder class in nonparametric regression estimation with fixed
design.
Bibliography
When and where
Face-to-face lectures
Learning assessment procedures
There is both the possibility of taking a written assessment test in classical form with questions related to topics covered in lectures and the possibility of writing a report on findings from the recent literature on nonparametric statistical inference.
Assessment
In evaluating the report and the final discussion, the capacity for analysis, methodological rigor and autonomy demonstrated by the Ph.D. candidate will be taken in account.
Criteria for the composition of the final grade
The final grade results from the report grade and a brief discussion/review of the report.
Scheduled Lessons
| When | Classroom | Teacher | topics |
|---|---|---|---|
|
Tuesday 03 October 2023 15:00 - 18:00 Duration: 3:00 AM |
Polo Santa Marta - SMT.04 [SMT.4 - terra] | Catia Scricciolo | Mathematical Statistics |
|
Tuesday 10 October 2023 15:00 - 18:00 Duration: 3:00 AM |
Polo Santa Marta - SMT.04 [SMT.4 - terra] | Catia Scricciolo | Mathematical Statistics |
|
Tuesday 17 October 2023 15:00 - 18:00 Duration: 3:00 AM |
Polo Santa Marta - SMT.04 [SMT.4 - terra] | Catia Scricciolo | Mathematical Statistics |
|
Tuesday 24 October 2023 15:00 - 18:00 Duration: 3:00 AM |
Polo Santa Marta - SMT.04 [SMT.4 - terra] | Catia Scricciolo | Mathematical Statistics |
|
Monday 30 October 2023 15:00 - 18:00 Duration: 3:00 AM |
Polo Santa Marta - SMT.04 [SMT.4 - terra] | Catia Scricciolo | Mathematical Statistics |
|
Tuesday 07 November 2023 15:00 - 18:00 Duration: 3:00 AM |
Polo Santa Marta - SMT.04 [SMT.4 - terra] | Catia Scricciolo | Mathematical Statistics |
|
Monday 13 November 2023 16:00 - 18:00 Duration: 1:50 AM |
Polo Santa Marta - Sala Andrea Vaona (DSE) [1.59 - 1] | Catia Scricciolo | Mathematical Statistics |
|
Tuesday 19 December 2023 14:00 - 18:00 Duration: 12:10 AM |
Polo Santa Marta - SMT.07 [SMT.7 - terra] | Catia Scricciolo | EXAM: Mathematical Statistics |
PhD school courses/classes - 2023/2024
Please note: Additional information will be added during the year. Currently missing information is labelled as “TBD” (i.e. To Be Determined).
PhD students must obtain a specified number of CFUs each year by attending teaching activities offered by the PhD School.
First and second year students must obtain 8 CFUs. Teaching activities ex DM 226/2021 provide 5 CFUs; free choice activities provide 3 CFUs.
Third year students must obtain 4 CFUs. Teaching activities ex DM 226/2021 provide 2 CFUs; free choice activities provide 2 CFUs.
Registering for the courses is not required unless explicitly indicated; please consult the course information to verify whether registration is required or not. When registration is actually required, no confirmation e-mail will be sent after signing up.
Teaching Activities ex DM 226/2021: Linguistic Activities
INFORMATION: ENGLISH FOR ACADEMIC PRESENTATION SKILLS [Arts and Humanities]
Credits: 2,5
Language: English
INFORMATION: ENGLISH FOR ACADEMIC PRESENTATION SKILLS [Law and Economics]
Credits: 2,5
Language: English
INFORMATION: ENGLISH FOR ACADEMIC PRESENTATION SKILLS [Life and Health Sciences - 1 st Session]
Credits: 2,5
Language: English
INFORMATION: ENGLISH FOR ACADEMIC PRESENTATION SKILLS [Life and Health Sciences - 2 nd Session]
Credits: 2,5
Language: English
INFORMATION: ENGLISH FOR ACADEMIC PRESENTATION SKILLS [Natural Sci. and Engineering-1st Session]
Credits: 2,5
Language: English
INFORMATION: ENGLISH FOR ACADEMIC PRESENTATION SKILLS [Natural Sci. and Engineering-2nd Session]
Credits: 2,5
Language: English
INFORMATION: ENGLISH FOR ACADEMIC WRITING SKILLS [Arts and Humanities]
Credits: 2,5
Language: English
INFORMATION: ENGLISH FOR ACADEMIC WRITING SKILLS [Law and Economics]
Credits: 2,5
Language: English
INFORMATION: ENGLISH FOR ACADEMIC WRITING SKILLS [Life and Health Sciences - 1 st Session]
Credits: 2,5
Language: English
INFORMATION: ENGLISH FOR ACADEMIC WRITING SKILLS [Life and Health Sciences - 2 nd Session]
Credits: 2,5
Language: English
INFORMATION: ENGLISH FOR ACADEMIC WRITING SKILLS [Natural Sci. and Engineering-1st Session]
Credits: 2,5
Language: English
INFORMATION: ENGLISH FOR ACADEMIC WRITING SKILLS [Natural Sci. and Engineering-2nd Session]
Credits: 2,5
Language: English
Teaching Activities ex DM 226/2021: Research management and Enhancement
SEMINARIO AVANZATO SULLE RISORSE BIBLIOTECARIE PER LA RICERCA [Arts and Humanities]
Credits: 2,5
Language: Italian
Teacher: Donatella Boni
SEMINARIO AVANZATO SULLE RISORSE BIBLIOTECARIE PER LA RICERCA [Law and Economics]
Credits: 2,5
Language: Italian
Teacher: Luisella Zocca
SEMINARIO AVANZATO SULLE RISORSE BIBLIOTECARIE PER LA RICERCA [Scientific Area]
Credits: 2,5
Language: Italian
Teacher: Elena Scanferla
Teaching Activities ex DM 226/2021: Statistics and Computer Sciences
INTRODUCTION TO PROBABILITY (MODULE I)
Credits: 1
Language: English
Teacher: Marco Minozzo
INTRODUCTION TO PROBABILITY (MODULE II)
Credits: 1
Language: English
Teacher: Marco Minozzo
BASIC LEVEL STATISTICS
Credits: 2,5
Language: English
INTRODUCTION TO STATISTICAL INFERENCE
Credits: 1
Language: English
Validità e affidabilità delle misure e dei test diagnostici
Credits: 0,5
Language: English
Teacher: Alessandro Marcon
BASIC LEVEL STATISTICS
Credits: 2,5
Language: Italian
Statistical analysis with R - module I
Credits: 1
Language: Italian
Teacher: Erica Secchettin
Generalized linear models: logistic regression, loglinear model, Poisson model
Credits: 2
Language: English
Teacher: Lucia Cazzoletti
Disegno dello studio nella ricerca osservazionale e sperimentale
Credits: 1,5
Language: English
Teacher: Alessandro Marcon
Calcolo della numerosità campionaria in funzione di una precisione o potenza statistica prefissata
Credits: 1
Language: English
Teacher: Giuseppe Verlato
Introduzione alla meta-analisi per la ricerca biomedica (revisione della letteratura, raccolta dei dati, costruzione del database)
Credits: 1
Language: English
Teacher: Giuseppe Verlato
Applicazioni della meta-analisi in campo epidemiologico e medico
Credits: 1
Language: English
Teacher: Giuseppe Verlato
Analisi di sopravvivenza: test log-rank, curve di sopravvivenza di Kaplan-Meier, modello di regressione di Cox
Credits: 1,5
Language: Inglese - English
Teacher: Simone Accordini
INTERMEDIATE STATISTICS [Recommended for Human Sciences]
Credits: 2,5
Language: English
INTERMEDIATE STATISTICS [Tutti i corsi di studio]
Credits: 2,5
Language: English
Statistical analysis with R - module II
Credits: 2
Language: Italian
Teacher: Erica Secchettin
Teaching Activities: Free choice
PROTECTING PSYCHOLOGICAL WELL-BEING IN THE PHD PROGRAM: WHAT DO WE NEED TO CONSIDER FOR BEING A GOOD SCIENTIST: BEST PRACTICE AND THE ETHICS OF SCIENCE
Credits: 1
Language: inglese
Teacher: Paola Cesari
QUANDO LA RICERCA SI FA ETICA (PERCORSO ORGANIZZATO E FINANZIATO DAL TEACHING AND LEARNING CENTER DI UNIVR)
Credits: 2
Language: Italian
Teacher: Roberta Silva
IMPARA IL MARKETING DIGITALE
Credits: 1,5
Language: English
Italian Poetry abroad
Credits: 1
Language: Italiano
Teacher: Massimo Natale
COSTRUISCI IL TUO BUSINESS MODEL CANVAS
Credits: 1,5
Language: English
APPROCCI E METODOLOGIE PARTECIPATIVE NELLA RICERCA CON GLI ATTORI DEL TERRITORIO
Credits: 1,5
Language: Italian
Teacher: Cristiana Zara
DOING INTERVIEWS IN QUALITATIVE RESEARCH
Credits: 1,5
Language: English
Teacher: Chiara Sità
LA COMUNICAZIONE UMANISTICA: OPPORTUNITA' E RISCHI
Credits: 1
Language: Italiano
DIFFERENTIAL DIAGNOSIS OF DEMYELINATING DISEASES OF THE CENTRAL NERVOUS SYSTEM
Credits: 2
Language: English
Teacher: Alberto Gajofatto
IL SONNO E I SUOI DISTURBI: FOCUS SULLE PARASONNIE E I DISTURBI DEL MOVIMENTO IN SONNO
Credits: 1
Language: English
Teacher: Elena Antelmi
IMAGING TECHNIQUES FOR BODY COMPOSITION ANALYSIS
Credits: 1
Language: English
Teacher: Carlo Zancanaro
OPEN SCIENCE: THE MIGHTY STICK AGAINST "BAD" SCIENCE
Credits: 2
Language: English
Teacher: Alberto Scandola
THE EMPIRICAL PHENOMENOLOGICAL METHOD (EPM): THEORETICAL FOUNDATION AND EMPIRICAL APPLICATION IN EDUCATIONAL AND HEALTHCARE FIELDS
Credits: 2
Language: English
THE PATHWAY OF OXYGEN: CAUSE OF HYPOXEMIA
Credits: 1
Language: English
Teacher: Carlo Capelli
Faculty
045 802 8102
simona.fiore@univr.it
tamara.fioroni@univr.it
cecilia.mancini@univr.it
andrea.mazzon@univr.it
martina.menon@univr.it
marcella.veronesi@univr.it
giorgio.vocalelli@univr.it
PhD students
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Guidelines for PhD students
Below you will find the files that contain the Guidelines for PhD students and rules for the acquisition of ECTS credits (in Italian: "CFU") for the Academic Year 2023/2024.
Documents
| Title | Info File |
|---|---|
Guidelines PhD students
|
pdf, en, 334 KB, 19/04/24 |
|
Linee guida dottorandi
|
pdf, it, 251 KB, 19/04/24 |
|
Percorso formativo
|
pdf, it, 283 KB, 19/04/24 |
|
Training program
|
pdf, en, 358 KB, 19/04/24 |
