ASYMPTOTICALLY EFFICIENT MEDIAN REGRESSION IN THE PRESENCE OF HETEROSKEDASTICITY OF UNKNOWN FORM

By Quanshui Zhao. Econometric Theory, 2001

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A Lack-of-Fit Test for Quantile Regression (2003, background): “For the more general case (11), Zhao (2001) showed that the scale function s.x/ can be consistently estimated using a nearest-neighbor approach and that the resulting reweighted quantile estimate is also rst-order equivalent to that with a known s.x/.”
Quantile regression with varying coefficients (2007, background): “For general s(Ti,Xi), Zhao [36] showed that s(Ti,Xi) can be consistently estimated using a nearest neighbor approach and that the resulting weighted quantile estimator is first-order equivalent.”
Estimation of counterfactual distributions using quantile regression (2006, methodology): “The efficiency of the parametric estimator can certainly be improved by using weighted quantile regression (Zhao 1999).”
Quantiles for Counts (2002, background): “Naturally, the efficiency of the QR estimators could also be improved using appropriate weights (see Newey and Powell 1990; Koenker and Zhao 1994; Zhao 2001), but that idea is not pursued here.”
Smoothing Quantile Regressions (2019, methodology): “Before stating the result, recall that Newey and Powell (1990) show that q(τ ) := τ(1 − τ)D−1q (τ ), with Dq(τ ) := E [ XX′ q2(τ”
Quantile regression methods for recursive structural equation models (2004, background): “We will not address the somewhat delicate issues involved in estimating weights, but the interested reader could consult Koenker and Zhao (1994) and/or Zhao (2001).”