In our study we extend the classical Analysis of Covariance (ANCOVA) for testing parallelism of lines between groups to nonparametric ANCOVA for testing the equality or parallelism of multiple regression curves. Our approach is based on local polynomial regression and extends the nonparametric F-tests in Huang and Chen (2008). We derive explicit expressions for the nonparametric ANCOVA table and develop nonparametric F-tests for testing the equality or parallelism of multiple curves based on assumptions of a common range of design points, homoscedastic Gaussian errors, and the same bandwidth and kernel function for fitting the curves. Simulation results indicate that the new approach is comparable to existing procedures.

In our study we extend the classical Analysis of Covariance (ANCOVA) for testing parallelism of lines between groups to nonparametric ANCOVA for testing the equality or parallelism of multiple regression curves. Our approach is based on local polynomial regression and extends the nonparametric F-tests in Huang and Chen (2008). We derive explicit expressions for the nonparametric ANCOVA table and develop nonparametric F-tests for testing the equality or parallelism of multiple curves based on assumptions of a common range of design points, homoscedastic Gaussian errors, and the same bandwidth and kernel function for fitting the curves. Simulation results indicate that the new approach is comparable to existing procedures.

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