Estimation of Semiparametric Models When the Criterion Function is Not Smooth

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Non-Parametric Regression for Binary Dependent Variables (2006, methodology): “In the context of local likelihood estimation, Staniswalis (1989) suggested a different crossvalidation criterion based on maximizing the leave-one-out fitted likelihood function CVM L (h, λ) = n∑ i=1 Yi ln g(Xi , θ̂−Xi |h,δ,λ) + (1 − Yi ) ln(1 − g(Xi , θ̂−Xi |h,δ,λ)).”
Specification Tests of Parametric Dynamic Conditional Quantiles (2010, unknown): “Theorem 3 in Chen et al. (2003) and A3 yield that (20) holds for such partition.”
Semiparametric Efficiency in GMM Models of Nonclassical Measurement Errors, Missing Data and Treatment Effects (2008, unknown): “We establish this theorem by applying Theorem 1 in Chen, Linton, and van Keilegom (2003)(hereafter CLK) with their θ being our β and their h being our p().”
Locally Robust Semiparametric Estimation (2016, methodology): “The choice of  = 5 works well based on a variety of empirical examples and in simulations, for medium sized data sets of a few thousand observations; see Chernozhukov et al. (2018). The choice  = 10 works well for small data sets with the larger  providing more observations for construction of ̂”