Testing lack of fit in multiple regression

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Restricted likelihood ratio lack‐of‐fit tests using mixed spline models (2004, methodology): “A similar ‘max’ test statistic using orthogonal series estimators in multivariate regression models has been constructed by Aerts, Claeskens and Hart (2000) .”
The Focused Information Criterion (2003, methodology): “the AIC-based order selection tests of Eubank and Hart (1992) and Aerts, Claeskens and Hart (1999, 2000) , the BIC-type test statistic of Ledwina (1994), and the general goodness-of-fit tests of Claeskens and Hjort (2003).”
Goodness of Fit via Non‐parametric Likelihood Ratios (2004, methodology): “The second type of test keeps a fixed C value and rejects when Z n exceeds a positive constant z0, and is similar in spirit to tests used in regression models by Aerts et al. (2000).”
Goodness-of-Fit Tests for Parametric Regression Models (2001, background): “…criterion in d-dimensions, Stute, González Mantoiga, and Presedo Quindimil (1998) investigated a marked empirical process based on the residuals and Aerts, Claeskens, and Hart (1999) constructed tests based on orthogonal series that involved choosing a nested model sequence in the bivariate…”