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 mathematical properties of common mean estimators
Estimates and estimators of a parameter and criteria to evaluate them
Examples of variance estimation and mathematical properties of common variance estimators
Confidence interval for the mean
Examples of confidence intervals for the mean, with detailed derivations of their properties
Confidence intervals, confidence coefficients, how to evaluate them
Confidence interval for the variance
Examples of confidence intervals for the variance, with detailed derivations of their properties
Testing hypotheses about the mean
Examples of hypothesis tests about the mean, with detailed derivations of their properties
Null and alternative hypothesis, types of errors, size and power
Testing hypotheses about the variance
Examples of hypothesis tests about the variance, with detailed derivations of their properties
Introduction to estimators used in mathematical statistics, including ML, GMM, NLS
MLE - Covariance matrix estimation
How to estimate the covariance matrix of a maximum likelihood estimator
The fundamentals of the theory of maximum likelihood estimation
How to carry out tests of hypothesis in a maximum likelihood framework
How to solve numerically the maximum likelihood optimization problem
A test of hypothesis involving only restricted ML estimates
A test of hypothesis involving only unrestricted ML estimates
Criteria used to select the best model among a set of candidate models estimated by ML
A test of hypothesis involving both restricted and unrestricted ML estimates
Recursive algorithm used for ML estimation of latent-variable models
Exponential family of distributions
Parametric families that are particularly important in maximum likelihood estimation
The fundamentals of conditional models, regression and classification
Properties of the OLS estimator
Asymptotic properties of the OLS estimators of regression coefficients
Introduction to the mathematics of linear regression models: notation, assumptions, inference.
R squared of a linear regression
A measure of how well a linear regression fits the data
The Normal Linear Regression Model
A regression model in which errors are conditionally normal
The OLS estimator is the best among those that are linear and unbiased
Linear regression - Hypothesis testing
How to test hypotheses about coefficients estimated by OLS
Standardized linear regression
Linear regression where all the variables are centered and divided by their standard deviation
How to estimate the regression coefficients efficiently when the errors are heteroskedastic or correlated
A biased estimator of linear regression coefficients whose MSE can be lower than that of OLS
If regressors are highly correlated, then OLS coefficient estimates have high variance
How to separately estimate the regression coefficients of two groups of regressors
Variables used in regression models to encode categorical features
Use our calculator to run your regressions effortlessly and without coding
Binary classification model in which the logistic function is used to transform inputs
Conditional models in which the output variable has a discrete distribution
Binary model in which the cdf of a standard normal distribution is used to transform inputs
Definition of autocorrelation, autocorrelation function (ACF), sample ACF, ACF plots.
Sequences of random vectors whose future does not depend on the past conditional on the present
How to diagnose (and solve) problems with MCMC samples
Monte Carlo methods based on sequences of dependent draws from a distribution
MCMC algorithm based on acceptance/rejection of draws from a proposal distribution
Bayesian models in which the parameters of the prior are assigned a hyper-prior
The fundamentals of Bayesian inference: prior, likelihood, posterior distributions
Bayesian inference about the parameters of a normal linear regression model
Normal distribution - Bayesian estimation
Bayesian inference about the parameters of a normal distribution
A simple and intuitive way of comparing two different models or hypotheses
When prior and posterior distribution belong to the same parametric family
An "objective" prior that has little influence on the posterior distribution
A scale used to translate the value of the Bayes factor into a qualitative judgement on the evidence
Most of the learning materials found on this website are now available in a traditional textbook format.
