Testing conditional monotonicity in the absence of smoothness
AbstractThis article proposes an omnibus test for monotonicity of nonparametric conditional distributions and its moments. Unlike previous proposals, our method does not require smooth estimation of the derivatives of nonparametric curves and it can be implemented even when the probability densities do not exist. In fact, we only require continuity of the marginal distributions. Distinguishing features of our approach are that the test statistic is pivotal under the null and invariant to any monotonic continuous transformation of the explanatory variable in finite samples. The test statistic is the sup-norm of the difference between the empirical copula function and its least concave majorant with respect to the explanatory variable coordinate. The resulting test is able to detect local alternatives converging to the null at the parametric rate n-1/2; like the classical goodness-of-.t tests. The article also discusses restricted estimation procedures under monotonicity and extensions of the basic framework to general conditional moments, estimated parameters and multivariate explanatory variables. The finite sample performance of the test is examined by means of a Monte Carlo experiment.
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Bibliographic InfoPaper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we1017.
Date of creation: Mar 2010
Date of revision:
Stochastic monotonicity; Conditional moments; Least concave majorant; Copula process; Distribution-free in finite samples; Tests invariant to monotone transforms;
Other versions of this item:
- Delgado, Miguel A. & Escanciano, Juan Carlos, . "Testing conditional monotonicity in the absence of smoothness," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/9136, Universidad Carlos III de Madrid.
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
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- Denis Chetverikov, 2012. "Testing regression monotonicity in econometric models," CeMMAP working papers CWP35/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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