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Program

EN IT

Updated A.Y. 2022-2023

The course is an introduction to the fundamental principles and tools of statistical inference, i.e. how to draw conclusions from
data subject to random variation. Topics include: random sampling; principles of data reduction; point and interval estimation (likelihood theory); hypothesis testing; confidence intervals and notes on nonparametric inference.

In Particular:

Brief review of probability


Random samples and asymptotic methods

  • Sampling and sums of random variables
  • Laws of large numbers and central limit theorem

Principles of Data Reduction

The Likelihood Principle: the Likelihood Function.

Point Estimation

  • Methods of Finding Estimators: Methods of Moments, Maximum Likelihood Estimators
  • Evaluation of estimators: Unbiasedness, Consistency, Fisher Information and the Cramer-Rao theorem.
  • Confidence Intervals

Hypothesis Testing

  • Methods of Finding Tests: Neyman Pearson lemma
  • Large sample tests: Likelihood Ratio Tests, Score Test, Wald Test 
  • Methods of Evaluating Tests: the Power Function, Most Powerful Tests.
  • The p-value.

Notes on Bayesian Inference

Non Parametric Inference

  • Kolmogorov-Smirnov Test

LEARNING OUTCOMES:

The course is designed to provide an in-depth knowledge of the main aspects of statistical inference (point estimation and hypothesis testing), both from a conceptual and a technical point of view. Tecniques for small and large samples will be provided. 


KNOWLEDGE AND UNDERSTANDING: The student is expected to learn the main inferential tecniques and to acquire  the tools to evaluate the goodness of the different methods.

APPLYING KNOWLEDGE AND UNDERSTANDING
At the end of the course the student will be able to formalize pratical probelms and solve specific analytical problems such as finding and comparing estimators, comparing different inferential methods and implementing hypotheis testing tecniques. 

MAKING JUDGEMENTS: 
At the end of the course, the students will be able to apply the knowledge learned and to critically interpret quantitative data related to economic and financial phenomena.

COMMUNICATION SKILLS:
Students will acquire the technical language typical of statistics and be able to comunicate in a clear and unambiguous way the concepts learned during the course.

 

LEARNING SKILLS:
At the end of the course the students will be able to formalize and to solve pratical problems, showing to be able to implement independently the methods learned.