Testing conditional monotonicity in the absence of smoothness

Miguel Delgado () and Juan Carlos Escanciano

UC3M Working papers. Economics from Universidad Carlos III de Madrid. Departamento de Economía

Abstract: This 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.

Keywords: Stochastic; monotonicity; Conditional; moments; Least; concave; majorant; Copula; process; Distribution-free; in; finite; samples; Tests; invariant; to; monotone; transforms (search for similar items in EconPapers)
JEL-codes: C14 C15 (search for similar items in EconPapers)
Date: 2010-03
New Economics Papers: this item is included in nep-ecm
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:cte:werepe:we1017

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