Learn the mathematical foundations of statistics, through a series of rigorous but accessible lectures on the most frequently utilized statistical concepts.
Samples, statistical models, estimation, statistical decisions
Examples of mean estimation and properties of common mean estimators
Estimates and estimators of a parameter and criteria to evaluate them
Examples of variance estimation and properties of common variance estimators
Examples of confidence intervals for the mean, with detailed derivations of their properties
Confidence intervals, confidence coefficients, how to evaluate them
Examples of confidence intervals for the variance, with detailed derivations of their properties
Examples of hypothesis tests about the mean, with detailed derivations of their properties
Null and alternative hypothesis, types of errors, size and power
Examples of hypothesis tests about the variance, with detailed derivations of their properties
Introduction to extremum estimators, including ML, GMM, NLS
How to estimate the covariance matrix of a maximum likelihood estimator
Maximum likelihood estimators and their asymptotic properties
How to carry out tests of hypothesis in a maximum likelihood framework
How to solve numerically the ML optimization problem
A test of hypothesis involving only restricted ML estimates
A test of hypothesis involving only unrestricted ML estimates
A test of hypothesis involving both restricted and unrestricted ML estimates
Introduction to conditional models, regression and classification
Asymptotic properties of the OLS estimators of regression coefficients
Introduction to linear regression models: notation, assumptions, inference.
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