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Notes: These teaching resources correspond to the course "Statistique Mathématique" (in French) of the first year program of the Master ESA (Université of Orléans).
Chapters
Chapters
Introduction_ESA.pdfGeneral introduction
General introduction
What is an econometrics?
Population and sample
Probability and random sampling
Cross-sectional data, time series data, and panel data
Parametric and semi-parametric models
Econometric model
Download the slides of the Syllabus
Chapter 1. Estimation Theory
Chapter 1. Estimation Theory
What is an estimator?
Finite sample and large sample properties of an estimator
Convergence: almost sure, probability, mean square, distribution
Law of large numbers and Central Limit Theorem
Continous mapping theorem and delta method
Asymptotic distribution of an estimator
Hurlin C. (2025), Estimation Theory, Master ESA, Université d'Orléans, Chapter 1.
Chapter1_Estimation_Theory_ESA.pdfChapter2_MLE_ESA.pdfChapter 2. Maximum Likelihood Estimation
Chapter 2. Maximum Likelihood Estimation
Likelihood function
Maximum Likelihood Estimator
Score, Gradient, and Hessian
Fisher information matrix
Asymptotic properties of the maximum likelihood estimator
Applications :multiple linear regression, probit and logit models
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Chapter 3. The Multiple Linear Regression Model
Chapter 3. The Multiple Linear Regression Model
The multiple linear regression model
Parametric and semi-parametric specifications
The Ordinary Least Squares (OLS) estimator
Statistical properties of the OLS
Finite and asymptotic sample properties of the OLS
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Chapter3_Linear_Model_ESA.pdfChapter4_Inference_ESA.pdfChapter 4. Statistical Hypothesis Testing
Chapter 4. Statistical Hypothesis Testing
Statistical hypothesis testing and inference
Tests in the multiple linear regression model
The Student t-test and Fisher test
Maximum Likelihood Estimation (MLE) and Inference
The Likelihood Ratio (LR), Wald and Lagrange Multiplier (LM) tests
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Chapter 5. Heteroscedasticity
Chapter 5. Heteroscedasticity
The generalized linear regression model
Generalized Least Squares (GLS)
Feasible Generalized Least Squares (FGLS)
Heteroscedasticity
White correction for heteroscedasticity
Testing for heteroscedasticity: Breusch-Pagan and White tests
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Chapter5_GLS_ESA.pdfChapter6_IV_ESA.pdfChapter 6. Endogeneity and Instrumental Variables
Chapter 6. Endogeneity and Instrumental Variables
Definition and source of endogeneity
Endogeneity bias of the OLS estimator
Endogenity biais and smearing effect
Instrumental variable
Instrumental Variables (IV) estimator
Two-Stage Least Squares (2SLS)
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Chapter 7. Bayesian Econometrics
Chapter 7. Bayesian Econometrics
Prior and posterior distribution
Posterior distributions and inference
Application to Bayesian VAR
Numerical simulations
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Chapter7_Bayesian.pdfExams
Exams
Mid-term exam 2015-2016 - Master ESA - Université d'Orléans (sujet) et (correction)
MLE and Gamma distribution
Wald test, LM test, LR test
Final exam 2020-2021 - Master ESA - Université d'Orléans (sujet) et (correction)
MLE and Logit model
Wald test, LM test, LR test
Mid-term exam 2021-2022 - Master ESA - Université d'Orléans (sujet) et (correction)
MLE and Weibull distribution
Wald test, LM test, LR test
Mid-term exam 2022-2023 - Master ESA - Université d'Orléans (sujet) et (correction)
AR model and maximum likelihood
z-tests in linear regression model
Wald test, LM test, LR test
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