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Testing Monotonicity of Regression Functions – An Empirical Process Approach
Author(s) -
BIRKE MELANIE,
NEUMEYER NATALIE
Publication year - 2013
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2012.00820.x
Subject(s) - mathematics , estimator , statistics , nonparametric regression , consistency (knowledge bases) , monotonic function , regression function , regression , regression analysis , kernel regression , kernel smoother , kernel (algebra) , econometrics , kernel method , computer science , artificial intelligence , mathematical analysis , geometry , combinatorics , radial basis function kernel , support vector machine
. We propose several new tests for monotonicity of regression functions based on different empirical processes of residuals and pseudo‐residuals. The residuals are obtained from an unconstrained kernel regression estimator whereas the pseudo‐residuals are obtained from an increasing regression estimator. Here, in particular, we consider a recently developed simple kernel‐based estimator for increasing regression functions based on increasing rearrangements of unconstrained non‐parametric estimators. The test statistics are estimated distance measures between the regression function and its increasing rearrangement. We discuss the asymptotic distributions, consistency and small sample performances of the tests.