Test of significance when data are curves

Jianqing Fan, Sheng Kuei Lin

Research output: Contribution to journalArticlepeer-review

171 Scopus citations


With modern technology, massive data can easily be collected in a form of multiple sets of curves. New statistical challenge includes testing whether there is any statistically significant difference among these sets of curves. In this article we propose some new tests for comparing two groups of curves based on the adaptive Neyman test and the wavelet thresholding techniques introduced earlier by Fan. We demonstrate that these tests inherit the properties outlined by Fan and that they are simple and powerful for detecting differences between two sets of curves. We then further generalize the idea to compare multiple sets of curves, resulting in an adaptive high-dimensional analysis of variance, called HANOVA. These newly developed techniques are illustrated by using a dataset on pizza commercials where observations are curves and an analysis of cornea topography in ophthalmology where images of individuals are observed. A simulation example is also presented to illustrate the power of the adaptive Neyman test.

Original languageEnglish (US)
Pages (from-to)1007-1021
Number of pages15
JournalJournal of the American Statistical Association
Issue number443
StatePublished - Sep 1 1998
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Adaptive Neyman test
  • Adaptive analysis of variance
  • Functional data
  • Repeated measurements
  • Thresholding
  • Wavelets


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