Course : Statistical Inference
Participants : BSc Mathematics and Data Science Institution : Sorbonne University Instructor : Dr. Tanujit Chakraborty Timeline : September, 2022 to December, 2022 Sessions : 60 Sessions Email: tanujit.chakraborty@sorbonne.ae 
Course Introduction:
The course is a classical advanced course in (parametric) Mathematical Statistics. General theory of point estimation is presented within which the notions of unbiasedness, consistency and optimality are studied. A particular attention is given to maximum likelihood estimation. The next topics to be treated are confidence intervals and hypothesis testing. The course ends with an account on the linear model. In the framework of the course, a series of computer labs will be run on the following topics: simulations of random variables (by inversion, rejection sampling and by the BoxMuller transform) and MonteCarlo methods in Statistics.
Course Objectives:
The course will help the students by:
 Prove GlivenkoCantelli Theorem and assess its fundamental character within Mathematical Statistics.
 Determine the laws of order statistics and of functions of order statistics.
 Infer the laws of the main statistics built from a gaussian random sample, including such the chisquared statistic and the Tstatistic.
 Articulate the notion of a dominated statistical model as well as that of unbiased and consistent estimator. Construct minimum variance unbiased estimator by the RaoBlackwell/LehmannScheffé procedure and efficient estimators in the sense of CramérRao.
 Prove efficiency properties of Maximum Likelihood Estimators.
 Construct exact and asymptotic confidence intervals, likelihood ratio tests, and goodness of fit tests (chisquared and KolmogorovSmirnov).
 Construct leastsquared estimators in the framework of the general linear model and prove their efficiency properties.
 Test generalized linear hypotheses on parameters of linear models.
 Represent ANOVA as a linear model and perform statistical inferences in these models.
 Computer Lab Classes using RStudio.
Evaluation Components:
The evaluation components for the Statistical Inference (SI) course will be as follows:
1) Mid Term Test1 : 15% ; 2) Mid Term Test2 : 15% ; 3) Project Work : 20% ; 4) End Term Test : 50%.
1) Mid Term Test1 : 15% ; 2) Mid Term Test2 : 15% ; 3) Project Work : 20% ; 4) End Term Test : 50%.
Textbooks & References:
• Rice, John A. (2006) Mathematical statistics and data analysis, Cengage Learning (Very Interesting Textbook)
• Casella, George, and Roger L. Berger (2002). Statistical inference, Cengage Learning (Nice Textbook)
• Wasserman, Larry (2004). All of statistics: a concise course in statistical inference, Springer.
• Shao, J. (2003). Mathematical Statistics, Springer.
• Shao, J. (2005). Mathematical Statistics: Exercises and Solutions, Springer.
• Casella, George, and Roger L. Berger (2002). Statistical inference, Cengage Learning (Nice Textbook)
• Wasserman, Larry (2004). All of statistics: a concise course in statistical inference, Springer.
• Shao, J. (2003). Mathematical Statistics, Springer.
• Shao, J. (2005). Mathematical Statistics: Exercises and Solutions, Springer.
Some Very Interesting Papers For Reading :
I would recommend all the participants to go through these research articles (mostly nonmathematical) along with the course. Please click on the paper name to view these outstanding and interesting paper:
1. Statistics  What are the most important statistical ideas of the past 50 years? (2021)
2. Data Science  50 Years of Data Science (2017)
3. Statistics Vs Data Science  The science of statistics versus data science: What is the future? (2021)
4. Statistics Vs Machine Learning  Prediction, Estimation, and Attribution (2020)
5. Future  The future of statistics and data science (2018)
1. Statistics  What are the most important statistical ideas of the past 50 years? (2021)
2. Data Science  50 Years of Data Science (2017)
3. Statistics Vs Data Science  The science of statistics versus data science: What is the future? (2021)
4. Statistics Vs Machine Learning  Prediction, Estimation, and Attribution (2020)
5. Future  The future of statistics and data science (2018)
Lecture Notes:
This is a 14 weeks course offered at SUAD. All the data analysis were done using R software. Class notes, Slides, data and code are available:
Week 1 : Course Outline & Recap of Fundamentals
Topic: Introduction to Statistical Inference 
