Talk:Heteroscedasticity-consistent standard errors

Arellano element
Arellano has developed a form of HC that accounts for serial correlation as well.

This is implemented in R as part of the plm package.

?vcovHC

vcovHC {plm}	R Documentation Robust Covariance Matrix Estimators

Description

Robust covariance matrix estimators a la White for panel models.

Details

vcovHC is a function for estimating a robust covariance matrix of parameters for a fixed effects or random effects panel model according to the White method (White 1980, 1984; Arellano 1987). Observations may be clustered by "group" ("time") to account for serial (cross-sectional) correlation.

All types assume no intragroup (serial) correlation between errors and allow for heteroskedasticity across groups (time periods). As for the error covariance matrix of every single group of observations, "white1" allows for general heteroskedasticity but no serial (cross-sectional) correlation; "white2" is "white1" restricted to a common variance inside every group (time period) (see Greene (2003), 13.7.1-2 and Wooldridge (2002), 10.7.2); "arellano" (see ibid. and the original ref. Arellano (1987)) allows a fully general structure w.r.t. heteroskedasticity and serial (cross-sectional) correlation.

Weighting schemes are analogous to those in vcovHC in package sandwich and are justified theoretically (although in the context of the standard linear model) by MacKinnon and White (1985) and Cribari-Neto (2004) (see Zeileis, 2004).

Arellano, Manuel (1987). "Computing Robust Standard Errors for Within-group Estimators." Oxford 806 Bulletin of Economics and Statistics 49, 431-434.

Croissant, Yves and Giovanni Millo (2008). "Panel data econometrics in R: The plm package." Journal of 829 Statistical Software 27 (2), 1-43. — Preceding unsigned comment added by 72.160.52.13 (talk) 14:47, 19 January 2016 (UTC)

Merger proposal
Huber-White standard errors is the same thing as this, so I propose that the contents of that article be merged into here. (That article is a stub, so it should be pretty easy to do. I don't have the time to do it myself at the moment.) -- Walt Pohl (talk) 07:06, 10 December 2007 (UTC)


 * Yes, you should just do this. If there is no additional information, juste make Huber-White page a redirect here. PDBailey (talk) 05:32, 16 February 2009 (UTC)


 * NO

any article with heteroscedasticity in the title is for a select group of cognoscenti, while huber white is a common name intelligble to a much wider audience.Cinnamon colbert (talk) 12:33, 9 June 2009 (UTC)

Merger done, with some rewriting of lead. Main stuff transferred was some additional references. Melcombe (talk) 14:05, 23 October 2009 (UTC)

Huber
So why is it called HUBER-White standard error? There's no reference on the first guy. — Preceding unsigned comment added by 134.155.146.98 (talk) 15:06, 7 October 2011 (UTC)
 * I've just added the seminal reference by Peter J. Huber to the 'References' section. I don't know enough about the history to add anything about his contribution to the article text. Qwfp (talk) 18:52, 7 October 2011 (UTC)

Clarity
This article now contains this passage: Assume that we are studying the linear regression model



Y = X \beta + U, \, $$

where X is the vector of explanatory variables and β is a k × 1 column vector of parameters to be estimated.

The ordinary least squares (OLS) estimator is



\widehat \beta_\text{OLS} = (\mathbb{X}' \mathbb{X})^{-1} \mathbb{X}' \mathbb{Y}. \, $$

where $$\mathbb{X}$$ denotes the matrix of stacked $$X_i'$$ values observed in the data.

One may surmise that X is a 1 × k vector, but we shouldn't have to surmise. Then later it says "$$\mathbb{X}$$ denotes the matrix of stacked $$X_i'$$ values observed". Presumably the "prime" means "transpose", so Xi is a k × 1 column vector and Xi&prime; is a 1 × k row vector. This is inconsistent with the initial notation in which X is a 1 × k vector, and nothing has been said about that change. And instead of saying "stacked" one could say $\mathbb X$ is the matrix whose ith row is $ X_i'$  for as many values of i as there are data points, and that would be clear.

Are there some readers who don't feel disrespected by this sort of thing? Michael Hardy (talk) 20:10, 28 April 2019 (UTC)


 * The article actually correctly identified $$\mathbf{X}$$ as the design matrix until changed it to the current wording on 17 November 2013. --bender235 (talk) 21:14, 15 November 2019 (UTC)