Simultaneous confidence bands for contrasts between several nonlinear regression curves

Xiaolei Lu and Satoshi Kuriki

Journal of Multivariate Analysis, 2017, vol. 155, issue C, 83-104

Abstract: We propose simultaneous confidence bands of the hyperbolic-type for the contrasts between several nonlinear (curvilinear) regression curves. The critical value of a confidence band is determined from the distribution of the maximum of a chi-square random process defined on the domain of explanatory variables. We use the volume-of-tube method to derive an upper tail probability formula of the maximum of a chi-square random process, which is asymptotically exact and sufficiently accurate in commonly used tail regions. Moreover, we prove that the formula obtained is equivalent to the expectation of the Euler–Poincaré characteristic of the excursion set of the chi-square random process, and hence conservative. This result is therefore a generalization of Naiman’s inequality for Gaussian random processes. As an illustrative example, growth curves of consomic mice are analyzed.

Keywords: Chi-square random process; Expected Euler-characteristic heuristic; Gaussian random field; Growth curve; Naiman’s inequality; Volume-of-tube method (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.jmva.2016.11.011

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