University of Illinois Urbana-Champaign

Comparison of several curves in the context of nonparametric regression

Amarasinghe, Upali Ananda

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Description

Title
Comparison of several curves in the context of nonparametric regression
Author(s)
Amarasinghe, Upali Ananda
Issue Date
1991
Doctoral Committee Chair(s)
Cox, Dennis D.
Department of Study
Statistics
Discipline
Statistics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Statistics
Language
eng
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.
Type of Resource
text
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http://hdl.handle.net/2142/21596
Copyright and License Information
Copyright 1991 Amarasinghe, Upali Ananda

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