Test of significance when data are curves

Jianqing Fan Sheng-Kuei Lin

Statistics Theory and Methods mathscidoc:1912.43275

Journal of the American Statistical Association, 93, (443), 1007-1021, 1998.9
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
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  title={Test of significance when data are curves},
  author={Jianqing Fan, and Sheng-Kuei Lin},
  booktitle={Journal of the American Statistical Association},
Jianqing Fan, and Sheng-Kuei Lin. Test of significance when data are curves. 1998. Vol. 93. In Journal of the American Statistical Association. pp.1007-1021. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113426315492835.
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