Nonparametric comparison of curves with dependent errors |
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Authors: | J. M. Vilar-Fernández W. González-Manteiga |
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Affiliation: | 1. Departamento de Matemáticas , Facultad de Informática , 15071, Univ. A Coru?a, Spain eijvilar@udc.es;3. Departamento de Estadística e I.O. , Facultad de Matemáticas , 15706, Univ. Santiago C., Spain |
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Abstract: | Suppose that data {(x l,i,n , y l,i,n ): l?=?1, …, k; i?=?1, …, n} are observed from the regression models: Y l,i,n ?=?m l (x l,i,n )?+?? l,i,n , l?=?1, …, k, where the regression functions {m l } l=1 k are unknown and the random errors {? l,i,n } are dependent, following an MA(∞) structure. A new test is proposed for testing the hypothesis H 0: m 1?=?·?·?·?=?m k , without assuming that {m l } l=1 k are in a parametric family. The criterion of the test derives from a Crámer-von-Mises-type functional based on different distances between {[mcirc]} l and {[mcirc]} s , l?≠?s, l, s?=?1, …, k, where {[mcirc] l } l=1 k are nonparametric Gasser–Müller estimators of {m l } l=1 k . A generalization of the test to the case of unequal design points, with different sample sizes {n l } l=1 k and different design densities {f l } l=1 k , is also considered. The asymptotic normality of the test statistic is obtained under general conditions. Finally, a simulation study and an analysis with real data show a good behavior of the proposed test. |
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Keywords: | Hypothesis testing Regression models Nonparametric estimators Dependent data |
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