# Comparison of several curves in the context of nonparametric regression

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 Title: Comparison of several curves in the context of nonparametric regression Author(s): Amarasinghe, Upali Ananda Doctoral Committee Chair(s): Cox, Dennis D. Department / Program: Statistics Discipline: Statistics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Statistics Abstract: Consider the model $y\sb{lj} = \mu\sb{l}(t\sb{j})$ + $\varepsilon\sb{lj}$, $l = 1,..,m$ and $j = 1,..,n,$ where $\varepsilon\sb{lj}$ are independent mean zero finite variance random variables. Under the above setting we test the hypotheses$H\sb0 : \mu\sb1 (t) {=..=}\ \mu\sb{m}(t)$ vs $H\sb{a} : \mu\sb{l}(t)$ are not all equal.Different procedures for testing the above hypotheses are studied. Test procedures are based on comparing estimates of the regression functions. Both smoothing spline and orthogonal series estimators are considered and the smoothing parameters are selected using Generalized Cross Validation criterion. Under some regularity conditions the asymptotic distributions of some of the test statistics are shown to be normal. Asymptotic power comparisons for the shift alternative are discussed. Comparison of regression curves in Bayesian nonparametric regression is also investigated. Issue Date: 1991 Type: Text Language: English URI: http://hdl.handle.net/2142/21596 Rights Information: Copyright 1991 Amarasinghe, Upali Ananda Date Available in IDEALS: 2011-05-07 Identifier in Online Catalog: AAI9210725 OCLC Identifier: (UMI)AAI9210725