Overview
Halbert Lynn White Jr. (1950–2012) was an econometrician at the University of California, San Diego (UCSD). He is best known for the heteroskedasticity-consistent (HC) sandwich covariance estimator (White 1980) and the quasi-maximum likelihood (QMLE) theory for misspecified models (White 1982), both published in Econometrica. These two papers together established the foundations of robust inference in econometrics and are among the most-cited works in the discipline. White also made foundational contributions to neural network approximation theory and non-parametric estimation.
Key Contributions / Features
- HC sandwich estimator (1980): V^(β^)=(X′X)−1Ω^(X′X)−1 where Ω^=∑iε^i2xixi′; consistent for the true covariance of the ordinary least squares (OLS) estimator under any form of heteroskedasticity with finite fourth moments. The "robust standard errors" reported in virtually all applied econometrics papers derive from this formula.
- White test for heteroskedasticity (1980): nR2∼χq2 test based on regressing squared OLS residuals on cross-products of regressors; consistent against any variance–covariate dependence.
- Quasi-MLE theory and pseudo-true parameters (1982): Under misspecification, the maximum likelihood estimator (MLE) converges to the pseudo-true parameter θ∗=argminKL(f0∥f(⋅;θ)); asymptotic distribution is N(0,A−1BA−1) with sandwich covariance; information matrix equality A=B holds iff the model is correctly specified.
- Information matrix test (1982): Test of A(θ^)≈B(θ^) as a general misspecification diagnostic; rejection indicates distributional misspecification.
- Neural network approximation (1989–1992): Showed that feedforward neural networks are universal approximators for Borel-measurable functions; provided asymptotic theory for neural network estimators.
- Textbook: Asymptotic Theory for Econometricians (1984, Academic Press); standard graduate reference for limit theory in econometrics.
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