Confidence Bands for Convex Median Curves using Sign-Tests

Dümbgen, Lutz (2007). Confidence Bands for Convex Median Curves using Sign-Tests. In: Cator, Eric A.; Jongbloed, Geurt; Kraaikamp, Cor; Lopuhaä, Hendrik P.; Wellner, Jon A. (eds.) Asymptotics: Particles, Processes and Inverse Problems: Festschrift for Piet Groeneboom. Lecture Notes - Monograph Series: Vol. 55 (pp. 85-100). Beachwood, Ohio, USA: Institute of Mathematical Statistics

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Suppose that one observes pairs (x1,Y1), (x2,Y2), ..., (xn,Yn), where x1 < x2 < ... < xn are fixed numbers while Y1, Y2, ..., Yn are independent random variables with unknown distributions. The only assumption is that Median(Yi) = f(xi) for some unknown convex or concave function f. We present a confidence band for this regression function f using suitable multiscale sign tests. While the exact computation of this band seems to require O(n4) steps, good approximations can be obtained in O(n2) steps. In addition the confidence band is shown to have desirable asymptotic properties as the sample size n tends to infinity.

Item Type:

Conference or Workshop Item (Paper)


08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Dümbgen, Lutz


Lecture Notes - Monograph Series


Institute of Mathematical Statistics




Lutz Dümbgen

Date Deposited:

04 Oct 2013 14:57

Last Modified:

28 Nov 2020 02:21

URI: (FactScience: 49605)

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