OPTIMAL MINIMAX RATES FOR NONPARAMETRIC SPECIFICATION TESTING IN REGRESSION MODELS

By E. Guerre, P. Lavergne. Econometric Theory, 2002

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Breaking the curse of dimensionality in nonparametric testing (2008, methodology): “Another approach looks at the uniform consistency of the test against a class of regular alternatives, see Spokoiny (1996), Horowitz and Spokoiny (2001), Guerre and Lavergne (2002), and essentially reaches the same conclusion.”
An updated review of Goodness-of-Fit tests for regression models (2013, background): “Thus, for Hölder, Sobolev, and Besov spaces with derivatives of order s ≥ p/4 and known s, the rate is n−2s/(4s+p) (see Ingster works and Guerre and Lavergne 2002).”
Consistent Tests of Conditional Moment Restrictions (2006, background): “theoretical approach for comparing them, see Fan and Li (2000) and Guerre and Lavergne (2002) .”
Regression discontinuity designs with unknown discontinuity points: Testing and estimation (2015, background): “Relevant literature in the classical speci cation test includes Ingster (1993) and Guerre and Lavergne (2002).”
Testing a parametric model against a nonparametric alternative with identification through instrumental variables (2004, background): “See, for example, Guerre and Lavergne (2002) and Horowitz and”
Data-Driven Rate-Optimal Specification Testing in Regression Models (2005, methodology): “For Example 1b, the proof of Assumtion W1(ii) uses the same Taylor expansion as in Guerre and Lavergne (2002) to build the Πs,h. Assumption W1(iii), for any given q̄, is a consequence of Assumption W1(iii) for q̄ = 1.”