BOOTSTRAP TEST FOR DIFFERENCE BETWEEN MEANS IN NONPARAMETRIC REGRESSION Academic Article uri icon

abstract

  • A bootstrap test is proposed for detecting a difference between two mean functions in the setting of nonparametric regression. Error distributions in the regression model are permitted to be arbitrary and unequal. The test enjoys power properties akin to those in a parametric setting, in the sense that it can distinguish between regression functions distant only n1/2apart, where n is the sample size. It has exceptional level accuracy, with level error of only n2, and uses a very accurate estimate of the critical point of an exact test, being in error by only n3/2under the null hypothesis. The test admits several generalizations, for example to the case of testing for differences between several regression means. (This is a nonparametric regression analog of analysis of variance.) A simulation study using n as small as 15 corroborates the asymptotic result on level accuracy of the bootstrap test. Applications are illustrated with an example involving acid rain data. 1990 Taylor & Francis Group, LLC.

published proceedings

  • JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION

author list (cited authors)

  • HALL, P., & HART, J. D.

citation count

  • 138

complete list of authors

  • HALL, P||HART, JD

publication date

  • December 1990