Data-Driven Rate-Optimal Specification Testing in Regression Models

By E. Guerre, P. Lavergne. 2005

89 citations recorded by the source corpus.

We propose new data-driven smooth tests for a parametric regression function. The smoothing parameter is selected through a new criterion that favors a large smoothing parameter under the null hypothesis. The resulting test is adaptive rate-optimal and consistent against Pitman local alternatives approaching the parametric model at a rate arbitrarily close to 1/sqrt(n). Asymptotic critical values come from the standard normal distribution and bootstrap can be used in small samples. A general formalization allows to consider a large class of linear smoothing methods, which can be tailored for detection of additive alternatives.

Subfields: Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3a0e66784f24fe512f78766724abe368200d1b12

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In Control and Systems Engineering

In Statistics and Probability

Citations in the corpus

TESTING FOR WHITE NOISE UNDER UNKNOWN DEPENDENCE AND ITS APPLICATIONS TO DIAGNOSTIC CHECKING FOR TIME SERIES MODELS (2010, background): “The latter problem has been well studied in the literature, and the data-driven bandwidth choice for the smoothing type test has been addressed in Horowitz and Spokoiny (2001) and Guerre and Lavergne (2005), among others.”
On Testing Independence and Goodness-of-fit in Linear Models (2013, background): “In [GL05] the authors propose data-driven smooth tests for a parametric regression function.”
Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors (2012, methodology): “Due to the space limitation, we put additional results and proofs into the SM [16].”
An updated review of Goodness-of-Fit tests for regression models (2013, methodology): “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). For unknown s, Spokoiny (1996) showed that the rate is (n−1 √ log logn)2s/(4s+p) and for s < p/4, it is shown in Guerre and Lavergne (2”
Towards data driven selection of a penalty function for data driven Neyman tests (2006, background): “50 [3]316 [5]149 [1]40 [7]23 [9]4 34 54 65 65 54 4 0.”
NONPARAMETRIC CONTROL CHART FOR MONITORING PROFILES USING CHANGE POINT FORMULATION AND ADAPTIVE SMOOTHING (2009, methodology): “This lemma can be proved easily by combining proofs in Hall and Marron (1990), about the Nadaraya-Watson estimator, with certain Lr-convergence properties of LLKE (Fan (1993) and Fan and Gijbels (1996)).”