Testing Monotonicity of Regression

Testing Monotonicity of Regression

We consider the problem of testing monotonicity of the regression function in a nonparametric regression model. We introduce test statistics that are functionals of a certain natural U-process. We study the limiting distribution of these test statistics through strong approximation methods and the e...

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Veröffentlicht in:The Annals of statistics 2000-08, Vol.28 (4), p.1054-1082
Hauptverfasser: Ghosal, Subhashis, Sen, Arusharka, van der Vaart, Aad W.
Format: Artikel
Sprache:eng
Schlagworte:
62G08
62G10
62G20
Approximation
Axiology
Empirical process
Exact sciences and technology
extreme values
Gaussian process
Linear inference, regression
Linear regression
Mathematical functions
Mathematical monotonicity
Mathematics
monotone regression
Nonparametric inference
Probabilities
Probability and statistics
Random variables
Sample size
Sciences and techniques of general use
Shape Restrictions in Regression
Statistical variance
Statistics
strong approximation
U-process
Umklapp process
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Beschreibung
Zusammenfassung:We consider the problem of testing monotonicity of the regression function in a nonparametric regression model. We introduce test statistics that are functionals of a certain natural U-process. We study the limiting distribution of these test statistics through strong approximation methods and the extreme value theory for Gaussian processes. We show that the tests are consistent against general alternatives.
ISSN:0090-5364
2168-8966
DOI:10.1214/aos/1015956707