Exercise Book of Statistical Inference

Francesca Gasperoni is currently employed in the pharmaceutical sector as trial statistician. Before moving to industry, she was a researcher at the MRC Biostatistics Unit (Cambridge, UK) and her research focussed on advanced statistical modelling for electronic heath records. During her PhD, obtained at Politecnico of Milan (Italy), she worked as teaching assistant for several courses of Probability and Statistics.Francesca Ieva is Associate Professor of Statistics at the Department of Mathematics of the Polytechnic of Milan. She deals with statistical learning in the biomedical field and statistical modeling for complex data coming from the world of healthcare research. Since 2021 she is associate head of the Health Data Science Center of Human Technopole.Anna Maria Paganoni is Full Professor of Statistics at the Department of Mathematics of the Polytechnic of Milan. She deals with statistical modeling and analysis of highly complex data with particular attention to the biomedical field and learning analytics. She is responsible for several competitively funded research projects. She is currently Coordinator of the Course of Studies in Mathematical Engineering, and delegate of the Rector for “Data Strategy”.

• Part I: Statistical Inference.- 1 Fundamentals of Probability and Statistics.- 2 Sufficient, Minimal, and Complete Statistics.- 3 Point Estimators.- 4 Uniform Minimum Variance Unbiased Estimators (UMVUEs).- 5 Likelihood Ratio Test.- 6 Uniformly Most Powerful Test.- 7 Confidence Intervals.- 8 Asymptotic Statistics.- Part II: Regression Models and Analysis of Variance.- 9 Linear Regression.- 10 Generalized Linear Models.- 11 ANOVA: Analysis of Variance.- 12 Summary Exercises.- Appendix A: Probability Distributions.