#### Abstract Details

 Activity Number: 129 - Quantile and Nonparametric Regression Models Type: Contributed Date/Time: Monday, July 31, 2017 : 8:30 AM to 10:20 AM Sponsor: Section on Nonparametric Statistics Abstract #322527 View Presentation Title: Shape Testing in Quantile Varying Coefficient Models with Heteroscedastic Error Author(s): Mohammed Abdulkerim Ibrahim* and Irène Gijbels and Anneleen Verhasselt Companies: Censtat, I-BioStat, Universiteit Hasselt and Department of Mathematics and Leuven Statistics Research Center (LStat), KU Leuven and Censtat, I-BioStat, Universiteit Hasselt Keywords: Heteroscedasticity ; Likelihood-ratio-test ; Qualitative shape testing ; Quantile regression ; Varying coefficient models Abstract: The interest is in regression quantiles in varying coefficient models for analyzing longitudinal data. The coefficients are allowed to vary with time, and the error variance (the variability function) varies with the covariates to allow for heteroscedasticity. The functional coefficients are estimated using penalized splines (P-splines), not requiring specification of the error distribution. A likelihood-ratio-type test is considered to test the shape (constancy, monotonicity and/or convexity) of the functional coefficients. Further, testing procedures based on $L_1$-norm, $L_2$-norm and $L_\infty$-norm of the differences of the P-splines coefficients are considered to test for constant functional coefficients. These norm based tests perform better than the likelihood-ratio-type test in our simulation study. An extreme value test for testing monotonicity or convexity, also performs better than the likelihood-ratio-type test. The likelihood-ratio-type test is, however, useful when testing the shape of the coefficients in signal and in variability function simultaneously. A real data example demonstrates the testing procedures.

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