Asymptotics in Statistics is a set of lectures within the course of Advanced Statistical Methods

for the Mathematics for daTa scieNce study plan

# Alessandra Salvan

Personal website
Bio Alessandra Salvan is professor of Statistics at the Department of Statistical Sciences of the University of Padova since 2002. At the same department, she has been Chair of the PhD School in Statistics, (2005-2012) and Head of Department (2011-2015). Her main research interests are: likelihood inference and asymptotics, treatment of nuisance parameters, inference based on pseudo-likelihoods for complex statistical models, model selection, conditional inference. Curriculum Vitae and publications ﻿are available at homes.stat.unipd.it/alessandrasalvan/sites/homes.stat.unipd.it.alessandrasalvan/files/cv_uk_2021_01_0.pdf.

# Nicola Sartori

Personal website
Bio Nicola Sartori is professor of Statistics at the Department of Statistical Sciences of the University of Padova since 2018. At the same department, he is currently Chair of the PhD School in Statistics. His main research interests are: likelihood and pseudo likelihood methods, likelihood asymptotics, statistical treatment of nuisance parameters, statistical computing. Curriculum Vitae and list of publications ﻿are available at: homes.stat.unipd.it/nicolasartori/sites/homes.stat.unipd.it.nicolasartori/files/cv_sartori_eng_new_2.pdf

## Prerequisites

• Probability
• Statistical Inference

## Aim

These set of lectures provide an introduction to the ideas and methods for the study of asymptotic approximations in statistics. These approximations are useful both to implement statistical procedures and to study their properties. Illustrative examples will be provided throughout.

## Syllabus

• Introduction and some preliminary notions.
Limit theorems and their use in Statistics. Moments, cumulants and their generating functions. Notations $O_p(\cdot)$ and $o_p(\cdot)$. Delta method, approximations of moments and transformations. Inversion of asymptotic series. Laplace approximation.
• Asymptotic expansions for distributions.
Generating functions of sums of independent random variables. Edgeworth and Cornish-Fisher expansions. Saddlepoint expansions.
• Asymptotic likelihood inference.
Statistical models and likelihood. Exponential and group families. Data and model reduction by marginalization and conditioning. First order and higher order inference.

## References

• Barndorff-Nielsen, O.E. and Cox, D.R. (1989). Asymptotic Techniques for Use in Statistics, Chapman and Hall.
• Barndorff-Nielsen, O.E. and Cox, D.R. (1994). Inference and Asymptotics. Chapman and Hall.
• Davison, A.C. (2003). Statistical Models. Cambridge University Press, Ch.12.
• Pace, L. and Salvan, A. (1997). Principles of Statistical Inference from a Neo-Fisherian Perspective, World Scientific.

## Schedule

• Friday, 16 April 2021 @ 15.30-18.30 (Nicola Sartori)
• Friday, 23 April 2021 @ 15.30-18.30 (Nicola Sartori)
• Friday, 30 April 2021 @ 15.30-18.30 (Alessandra Salvan)
• Friday, 07 May 2021 @ 15.30-18.30 (Alessandra Salvan)
• Friday, 14 May 2021 @ 15.30-18.30 (Alessandra Salvan)