A GOODNESS-OF-FIT TEST FOR SINGLE-INDEX MODELS

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An updated review of Goodness-of-Fit tests for regression models (2013, unknown): “…model, H0SIM is almost surely equivalent to E((Y − H(θ t0X))I(X ≤ x)) = 0, for all x ∈ Supp(X), and the empirical process is now given by ˜α̃n(x) = 1√ n n ∑ i=1 ε̂i0f̂̂θ ( ̂θ tXi ) I(Xi ≤ x), (25) whose asymptotic behavior was studied by Xia et al. (2004), jointly with different estimators for θ0.”
Model-based mean square error estimators for k-nearest neighbour predictions and applications using remotely sensed data for forest inventories (2009, methodology): “A goodness-of-fit test for the estimated function g was done according to Xia et al. (2004).”
Breaking the curse of dimensionality in nonparametric testing (2008, methodology): “Our focus was first to compare the small sample power of our test to the multivariate test of Zheng (1996) and Li and Wang (1998) and second to determine the sensitivity of our test to the penalty αn, the direction defined by β0 and the smoothing parameter h.”
SPLINE ESTIMATION OF SINGLE-INDEX MODELS (2009, background): “of �0. If this model is misspecified (m is not a genuine single-index function), however, a goodness-of-fit test then becomes necessary and the estimation of �0 must be rethought, see Xia, Li, Tong and Zhang (2004) .”