Checking the adequacy of a partial linear model

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Estimation for a partial-linear single-index model (2009, background): “ˆh opt, (3.2) respectively, because this guarantees that the required bandwidth has the correct order of magnitude for optimal asymptotic performance [see Carroll al.(1997), Stute and Zhu (2005), and Zhu and Ng (2003)]. Note that choices (3.2) satisfy condition C5(ii). Relevant discussion on choosin”
Nonparametric checks for single-index models (2005, methodology): “In a different setup, this algorithm has been used by Zhu [40] and Zhu and Ng [42].”
Model Checks Using Residual Marked Empirical Processes (2004, background): “…(1996), Stute (1997), Stute, Thies and Zhu (1998), Li and Wang (1998), Fan and Huang (2001), Horowitz and Spokoiny (2001), Li, Hsiao and Zinn (2003), Zhu (2003), Zhu and Ng (2003), Khmaladze and Koul (2004), Koul and Ni (2004), Escanciano (2006) and Guerre and Lavergne (2005), to mention a few.”
Empirical likelihood confidence regions in a partially linear single‐index model (2006, methodology): “As a by-product, this bias correction also sheds light on the nonparametric estimation procedure for model checking because, when √ n-consistency is needed, we often need undersmoothing (see Chen et al. (2003), Stute and Zhu (2002, 2005), Zhu (2003) and Zhu and Ng (2003)).”