Efficient estimation in conditional single-index regression

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Optimal rates and adaptation in the single-index model using aggregation (2007, unknown): “Among many other references, see Horowitz (1998) for applications in econometrics, an application in medical science can be found in Xia and H¨ardle (2006), see also Delecroix et al. (2003), Delecroix et al. (2006) and the survey paper by Geenens and Delecroix (2005).”
Successive direction extraction for estimating the central subspace in a multiple-index regression (2008, methodology): “We will say that the successive maximization is Fisher consistent (see, for example, Cox and Hinkley, 1974 ) if these vectors span the CS. If d = 0 no maximization is required and we say that the procedure is Fisher consistent by definition.”
Score estimation in the monotone single‐index model (2017, methodology): “Examples of this type are the semiparametric least-squares estimators (LSEs) of Ichimura (1993) and Härdle, Hall, and Ichimura (1993) and the pseudomaximum likelihood estimator of Delecroix, Härdle, and Hristache (2003), all using kernel regression estimates for the unknown link functions.”
On estimation efficiency of the central mean subspace (2014, background): “This allows us to derive the semiparametric efficient score, which has the potential of reaching the minimum estimation variance bound among all possible consistent estimators.”