# Shared Flashcard Set

## Details

ESM Statistics 1
Lectures 15-16, heteroskedasticity
40
Engineering
12/03/2011

Term
 Define "heteroskedasticity"
Definition
 when a collection of random variables has sub-populations. These sub-populations have different variabilities. In other words, the relationships between regressant and regressors are not the same throughout sample
Term
 Define "homoskedasticity"
Definition
 when a collection of random variables has no subpopulations; the variance is constant across the sample. In other words, on average the relationships between regressant and regressors are the same throughout sample
Term
 State the Gauss-Markov theorem
Definition
 β(ols) is the Best Linear Unbiased Estimator (BLUE) when:–ε~(0,σ^2*I(N)) -E(ε) = 0, -E(ε^2*I(N))is a symmetric matrix with constant diagonal terms and 0 for all off-diagonal terms-E(X'ε) = 0–The rank of X is K and K ≤ N)
Term
 What does "E(εi) =  0" mean?
Definition
 The residuals have a mean of 0
Term
 Define "residual"
Definition
 the difference between the sample and the estimated function value (from the regression)
Term
 What does "E(εi2) = σ" mean?
Definition
 The residuals are homoskedastic.
Term
 What does "E(εi*εj ) =  0    (i≠ j)" mean?
Definition
 There is no autocorrelation.
Term
 Define "autocorrelation"
Definition
 "When an analysis is correlated with itself" (**fix**)
Term
 What does "X's are nonstochastic with values fixed in repeated samples" mean?
Definition
 X's are deterministic, non-random; outcomes are consistent
Term
 Define "deterministic"
Definition
 no randomness is involved in the system; the same initial conditions always produces the same output
Term
 Define "stochastic"
Definition
 a system/process that is intrinsically non-deterministic. Randomness is involved!
Term
 What does "xi and εi are  uncorrelated" mean?
Definition
 X and the residuals are uncorrelated to each other
Term
 What does "The number of observations is greater than the number of parameters estimated" mean?
Definition
 There are more data points than unknown variables.
Term
 What does "No exact linear relationship exists between any of the explanatory variables" mean?
Definition
 There is no multicollinearity
Term
 Define "multicollinearity"
Definition
 when two or more predictor variables in a multiple regression model are highly correlated
Term
 What happens when εi are not identical for all i=(0,1,...,N)?
Definition
 heteroskedasticity
Term
 What happens if εi and εj are correlated for i /= j?
Definition
 autocorrelation
Term
 What effect does heteroskedasticity have on the OLS estimator?
Definition
 It remains unbiased and consistent, but coefficients are not efficient. Also standard errors are biased and inconsistent (effect: t statistics incorrect).
Term
 What is pure heteroskedasticity?
Definition
 Occurs due to the nature of the data.
Term
 What is impure heteroskedasticity?
Definition
 Occurs due to incorrect regression (ex: omitted variables)
Term
 Do heteroskedasticity tests distinguish between pure and impure types?
Definition
 No
Term
 Is this heteroskedastic or homoskedastic?  [image]
Definition
 Homoskedastic
Term
 Is this heteroskedastic or homoskedastic? [image]
Definition
 Heteroskedastic
Term
 Is this heteroskedastic or homoskedastic? [image]
Definition
 Heteroskedastic
Term
 How do you detect heteroskedasticity via plots?
Definition
 Estimate model, calculate the residuals, then plot the residuals against each variable separately.
Term
 Name four tests for homoskedasticity.
Definition
 Park test White test Breusch-Pagen test Goldfeld-Quandt test
Term
 Which three tests for heteroskedasticity use residual plots?
Definition
 White test* Breusch-Pagen test* Goldfeld-Quandt test *More commonly used
Term
 Which three tests for heteroskedasticity use residual plots?
Definition
 White test* Breusch-Pagen test* Goldfeld-Quandt test *More commonly used
Term
 Which three tests for heteroskedasticity use residual plots?
Definition
 White test* Breusch-Pagen test* Goldfeld-Quandt test *More commonly used
Term
 When can you use the Park test?
Definition
 When you know something about Σ (the error term)
Term
 Is this heteroskedastic or homoskedastic? [image]
Definition
 Heteroskedastic
Term
 Is this heteroskedastic or homoskedastic? [image]
Definition
 Homoskedastic
Term
 Is this heteroskedastic or homoskedastic? [image]
Definition
 Heteroskedastic
Term
 Is this heteroskedastic or homoskedastic? [image]
Definition
 Heteroskedastic
Term
 What are the steps of the Park test?
Definition
 [image]
Term
 When should you run a test for heteroskedasticity using a plot?
Definition
 When you do not have information about the error term (Σ is unknown)
Term
 What are the steps for the White test for heteroskedasticity?
Definition
 [image]
Term
 What is the modified version of the White test, and when/why would you use it?
Definition
 Same as standard White test except in the auxiliary regression, use only the x and x2 terms (no cross products). Use when you have many independent variables, as they make the White test much more complicated (example: 6 independent variables in regression -> 27 variables in White test auxiliary regression!)
Term
 What are two remedies for heteroskedasticity (after omitted variables has been ruled out)?
Definition
 -Corrected Standard errors-Generalized least squares (GLS)
Term
 How do you perform "Corrected Standard Errors" to correct for heteroskedasticity?
Definition
 [image]
Supporting users have an ad free experience!