|
Organizers |
Bootstrap tests for the equality of two regression functions by curve resampling
by
Hirohito Sakurai
Graduate School of Science and Technology, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, JAPAN
Coauthors: Masaaki Taguri (Faculty of Science, Chiba University, JAPAN)
We propose a bootstrap method for testing the equality of two regression functions in longitudinal data, where the data are generated from two independent groups. Our method is based on resampling from a set of curves by regarding each subject in longitudinal data as ``curve.'' In this paper we call this procedure ``curve resampling.'' If the lengths of all subjects are 1, curve resampling results in the naive bootstrap scheme.
Our problem is formulated as comparison of two regression functions (mean curves), which is therefore a generalization of comparing two means in two-sample problem. For two regression functions, f1(t) and f2(t), we consider the following hypothesis;
H0: f1(t) = f2(t) for all t vs. H1: not H0.
Then, our proposed bootstrap test consists of the following steps.
(1) Compute the value of test statistic based on the initial sample.
(2) Combine two groups of centered data.
(3) Draw two random samples corresponding to the two groups with replacement from the combined sample, and compute the value of test statistic based on the resamples.
(4) Repeating step (3) a certain number of times, reject the null hypothesis only when the achieved significance level is less than or equal to a given significance level.
In addition, permutation test using curve resampling is considered. The algorithm for this is obtained by changing the resampling method in the above testing algorithm, namely, in step (3), the resampling with replacement is changed to that without replacement.
In each testing procedure, three types of test statistics are considered to measure the difference of two regression functions. Monte Carlo simulations are carried out to investigate the size and power of the proposed tests.
Date received: October 12, 2000
Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafr-34.