Nonparametric models and methods for ancova with dependent data

The nonparametric ANCOVA model of Akritas et al. [Akritas, M. G., Arnold, S. F. and Du, Y. (2000). Nonparametric models and methods for nonlinear analysis of covariance. Biometrika, 87(3), 507-526.] is extended to longitudinal data and for up to three covariates. In this model the response distributions need not be continuous or to comply to any parametric or semiparametric model. The nonparametric covariate effect can be different in different factor level combinations. Nonparametric hypotheses of no main factor effects, no interaction and no simple effect, which adjust for the covariate values, are considered. The test statistics, which are based on averages over the covariate values of certain Nadaraya-Watson regression quantities, have asymptotically a central chi-squared distribution under their respective null hypotheses. Small sample corrections to the asymptotic distribution are provided. Simulation results and data analysis for a real dataset are presented.