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Testing for one-sided alternatives in nonparametric censored regression

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Testing for one-sided alternatives in nonparametric

cen-sored regression

C´

edric Heuchenne

1

and

Juan Carlos Pardo Fern´

andez

2

1

HEC-Management School of the University of Li`ege, University of Li`ege and Institut de statistique, Universit´e catholique de Louvain, Belgium

(e-mail: C.Heuchenne@ulg.ac.be)

2Department of Statistics and OR, University of Vigo, Spain

(e-mail: juancp@uvigo.es)

Abstract:

Assume we have two populations satisfying the general model Yj= mj(Xj) + εj, j = 1, 2, where m(·) is a smooth function, ε

has zero location and Yjis possibly right-censored. In this paper, we propose to test the null hypothesis H0: m1= m2versus

the one-sided alternative H1 : m1 < m2. We introduce two test statistics for which we obtain the asymptotic normality

under the null and the alternative hypotheses. Both tests can detect any local alternative converging to the null hypothesis at the parametric rate n−1/2. The practical performance of the tests is investigated in a simulation study. An application to a data set about unemployment is also included.

Keywords:

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