منابع مشابه
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 extreme value theory for Gaussian processes. We show that the tests are consistent against general...
متن کاملTesting of Monotonicity in Regression Models
In data anaysis concerning the investigation of the relationship between a dependent variable Y and an independent variable X, one may wish to determine whether this relationship is monotone or not. This determination may be of interest in itself, or it may form part of a (nonparametric) regression analysis which relies on monotonicity of the true regression function. In this paper we generaliz...
متن کاملTesting strict monotonicity in nonparametric regression
A new test for strict monotonicity of the regression function is proposed which is based on a composition of an estimate of the inverse of the regression function with a common regression estimate. This composition is equal to the identity if and only if the “true” regression function is strictly monotone, and a test based on an L2-distance is investigated. The asymptotic normality of the corre...
متن کاملwww.econstor.eu Testing strict monotonicity in nonparametric regression
A new test for strict monotonicity of the regression function is proposed which is based on a composition of an estimate of the inverse of the regression function with a common regression estimate. This composition is equal to the identity if and only if the “true” regression function is strictly monotone, and a test based on an L2-distance is investigated. The asymptotic normality of the corre...
متن کاملMonotonicity Testing
We present improved algorithms for testing monotonicity of functions. Namely, given the ability to query an unknown function f : E' -+ E, where E and E are finite ordered sets, the test always accepts a monotone f and rejects f with high probability if it is e-far from being monotone (i.e., if every monotone function differs from f on more than an E fraction of the domain). For any E > 0, the q...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2000
ISSN: 0090-5364
DOI: 10.1214/aos/1015956707