Testing for stochastic monotonicity

By S. Lee, Oliver B. Linton, Yoon-Jae Whang. 2006

90 citations recorded by the source corpus.

We propose a test of the hypothesis of stochastic monotonicity. This hypothesis is of interest in many applications. Our test is based on the supremum of a rescaled U-statistic. We show that its asymptotic distribution is Gumbel. The proof is difficult because the approximating Gaussian stochastic process contains both a stationary and a nonstationary part and so we have to extend existing results that only apply to either one or the other case.

Subfields: Economics and Econometrics, Sociology and Political Science

View Paper: https://www.semanticscholar.org/paper/bef4b5fdba53e78a4991ab278f2d155f62a2025e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In Sociology and Political Science

Citations in the corpus

Jackknife multiplier bootstrap: finite sample approximations to the U-process supremum with applications (2017, methodology): “U -processes are powerful tools for a broad range of statistical applications such as testing for qualitative features of functions in nonparametric statistics [38, 25, 1], cross-validation for density estimation [43], and establishing limiting distributions of M -estimators [see, e.”
TESTING FOR A GENERAL CLASS OF FUNCTIONAL INEQUALITIES (2013, methodology): “Our test can also be used as an alternative to testing monotonicity of mean regression (e.g., Chetverikov (2012) and Ghosal, Sen, and van der Vaart (2000)) as well as testing stochastic monotonicity (e.g., Lee, Linton, and Whang (2009) and Delgado and Escanciano (2012)).”
Doubly robust uniform confidence band for the conditional average treatment effect function (2016, methodology): “process using arguments built on Piterbarg (1996), combined with a Gaussian approximation result of Chernozhukov, Chetverikov, and Kato (2014) and an empirical process result of Ghosal, Sen, and van der Vaart (2000). Our method is simple to implement and does not rely on resampling techniques. This ”
TESTING REGRESSION MONOTONICITY IN ECONOMETRIC MODELS (2012, methodology): “An advantage of their method is that the asymptotic distribution of their test statistic in the least favorable model under H0 turns out to be N(0, 1), so that obtaining a critical value for their test is computationally very simple.”