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Testing monotone effects of covariates in nonparametric mixed models. (English) Zbl 1061.62068
Summary: In a multi-factorial nonparametric mixed model, an asymptotic rank-based test on monotone influence of a covariate is developed. Most methods available in the literature cannot handle data with ties or dependent observations. The procedure proposed here does not assume continuous distributions and is thus applicable to data with ties. It can be used even for ordinal or binary data. Also, it can handle dependent observation, as, for example, in longitudinal data. Moreover, the test developed in this paper, as well as the estimate of the regression parameter for the covariate, is easy to compute and does not require iterative algorithms. The method proposed here contains the test based on Spearman’s rank correlation coefficient as a special case. The finite sample performance of the test procedure is analyzed by computer simulations. Some examples illustrate the application.

MSC:
62G10 Nonparametric hypothesis testing
62J10 Analysis of variance and covariance (ANOVA)
62G20 Asymptotic properties of nonparametric inference
62G08 Nonparametric regression and quantile regression
Software:
GLIM
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