Lecture

Heteroskedasticity: Ch. 4a

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture by the instructor covers the concept of heteroskedasticity in econometrics, focusing on the issues related to standard errors when the assumptions of the Gauss-Markov model are violated. The lecture explains the impact of heteroskedasticity on OLS estimators and the need for alternative estimators like Generalized Least Squares (GLS). It discusses the simulation of heteroskedasticity, the problems it causes, and solutions such as Weighted Least Squares. The lecture also delves into testing for heteroskedasticity using Breusch-Pagan and White tests, the consequences of heteroskedasticity on hypothesis testing, and the use of heteroskedasticity-consistent standard errors in statistical analysis.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Official source

Ontological neighbourhood

Statistics

Data analysis: Regression analysis

Statistical inference: Mathematical statistics

Related concepts (32)

Generalized least squares

In statistics, generalized least squares (GLS) is a method used to estimate the unknown parameters in a linear regression model when there is a certain degree of correlation between the residuals in the regression model. Least squares and weighted least squares may need to be more statistically efficient and prevent misleading inferences. GLS was first described by Alexander Aitken in 1935. In standard linear regression models one observes data on n statistical units.

Weighted least squares

Weighted least squares (WLS), also known as weighted linear regression, is a generalization of ordinary least squares and linear regression in which knowledge of the unequal variance of observations (heteroscedasticity) is incorporated into the regression. WLS is also a specialization of generalized least squares, when all the off-diagonal entries of the covariance matrix of the errors, are null.

Least squares

The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each individual equation. The most important application is in data fitting.

Linear least squares

Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems involved in linear regression, including variants for ordinary (unweighted), weighted, and generalized (correlated) residuals. Numerical methods for linear least squares include inverting the matrix of the normal equations and orthogonal decomposition methods. The three main linear least squares formulations are: Ordinary least squares (OLS) is the most common estimator.

Linear regression

In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.

Related lectures (64)

Linear Regression: Estimation and Inference

Explores linear regression estimation, linearity assumptions, and statistical tests in the context of model comparison.

Linear Regression: Maximum Likelihood Approach

Covers linear regression topics including confidence intervals, variance, and maximum likelihood approach.

Linear Regression: Estimation and Testing

Explores linear regression estimation, hypothesis testing, and practical applications in statistics.

Linear Regression: Least Squares

Delves into linear regression, emphasizing least squares estimation, residuals, and variance.

Linear Regression Testing