Statistical Inference I

Ph.D. program in Economics, Statistics and Data Science.

Author

Affiliation

Alice Giampino

University of Milano-Bicocca

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Statistical Inference I provides an introduction to Statistical Inference, with a focus on point estimates. The course cover the problem of obtaining estimators for the parameters of a distribution, hypotheses testing and it ends with some basis knowledge on linear models.

Syllabus

• Introduction to statistical inference.

• Estimates and estimators: definitions and properties.

• The likelihood function and related quantities.

• Likelihood-based inference:

  • the maximum likelihood estimator (MLE) and its properties;

  • hypothesis testing.

  • likelihood-based confidence regions.

• Mathematical and computational tools to deal with the likelihood approach.

• Linear models.

Notes Lecture notes

Scripts

• Scrip 1: Estimators.

• Scrip 2: MLE - Normal.

• Scrip 3: Newton-Raphson - Gamma.

• Scrip 4: CI - Normal.

• Scrip 5: CI - Wald & LRT.

• Scrip 6: LM.

Textbooks

• Casella, G. and Berger, R.L., Statistical Inference, Second Edition.

• Everitt, B. and Hothorn, T, An Introduction to Applied Multivariate Statistics with R.

• Azzalini, A., Statistical Inference Based on the likelihood.

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