Goodness of fit test for isotonic regression

Cécile Durot; Anne-Sophie Tocquet

ESAIM: Probability and Statistics (2010)

  • Volume: 5, page 119-140
  • ISSN: 1292-8100

Abstract

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We consider the problem of hypothesis testing within a monotone regression model. We propose a new test of the hypothesis H0: “ƒ = ƒ0” against the composite alternative Ha: “ƒ ≠ ƒ0” under the assumption that the true regression function f is decreasing. The test statistic is based on the 𝕃 1 -distance between the isotonic estimator of f and the function f0, since it is known that a properly centered and normalized version of this distance is asymptotically standard normally distributed under H0. We study the asymptotic power of the test under alternatives that converge to the null hypothesis.

How to cite

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Durot, Cécile, and Tocquet, Anne-Sophie. "Goodness of fit test for isotonic regression." ESAIM: Probability and Statistics 5 (2010): 119-140. <http://eudml.org/doc/197737>.

@article{Durot2010,
abstract = { We consider the problem of hypothesis testing within a monotone regression model. We propose a new test of the hypothesis H0: “ƒ = ƒ0” against the composite alternative Ha: “ƒ ≠ ƒ0” under the assumption that the true regression function f is decreasing. The test statistic is based on the $\{\mathbb L\}_\{1\}$-distance between the isotonic estimator of f and the function f0, since it is known that a properly centered and normalized version of this distance is asymptotically standard normally distributed under H0. We study the asymptotic power of the test under alternatives that converge to the null hypothesis. },
author = {Durot, Cécile, Tocquet, Anne-Sophie},
journal = {ESAIM: Probability and Statistics},
keywords = {Nonparametric regression; isotonic estimator; goodness of fit test; asymptotic power.; asymptotic power},
language = {eng},
month = {3},
pages = {119-140},
publisher = {EDP Sciences},
title = {Goodness of fit test for isotonic regression},
url = {http://eudml.org/doc/197737},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Durot, Cécile
AU - Tocquet, Anne-Sophie
TI - Goodness of fit test for isotonic regression
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 5
SP - 119
EP - 140
AB - We consider the problem of hypothesis testing within a monotone regression model. We propose a new test of the hypothesis H0: “ƒ = ƒ0” against the composite alternative Ha: “ƒ ≠ ƒ0” under the assumption that the true regression function f is decreasing. The test statistic is based on the ${\mathbb L}_{1}$-distance between the isotonic estimator of f and the function f0, since it is known that a properly centered and normalized version of this distance is asymptotically standard normally distributed under H0. We study the asymptotic power of the test under alternatives that converge to the null hypothesis.
LA - eng
KW - Nonparametric regression; isotonic estimator; goodness of fit test; asymptotic power.; asymptotic power
UR - http://eudml.org/doc/197737
ER -

References

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