Goodness of fit test for isotonic regression

Cécile Durot; Anne-Sophie Tocquet

ESAIM: Probability and Statistics (2001)

  • 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 H 0 : “ f = f 0 ” against the composite alternative H a : “ f ≠ f 0 ” 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 f 0 , since it is known that a properly centered and normalized version of this distance is asymptotically standard normally distributed under H 0 . 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 (2001): 119-140. <http://eudml.org/doc/104269>.

@article{Durot2001,
abstract = {We consider the problem of hypothesis testing within a monotone regression model. We propose a new test of the hypothesis $H_\{0\}$: “$f=f_\{0\}$” against the composite alternative $H_\{a\}$: “$f\ne f_\{0\}$” 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 $f_\{0\}$, since it is known that a properly centered and normalized version of this distance is asymptotically standard normally distributed under $H_\{0\}$. 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},
language = {eng},
pages = {119-140},
publisher = {EDP-Sciences},
title = {Goodness of fit test for isotonic regression},
url = {http://eudml.org/doc/104269},
volume = {5},
year = {2001},
}

TY - JOUR
AU - Durot, Cécile
AU - Tocquet, Anne-Sophie
TI - Goodness of fit test for isotonic regression
JO - ESAIM: Probability and Statistics
PY - 2001
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 $H_{0}$: “$f=f_{0}$” against the composite alternative $H_{a}$: “$f\ne f_{0}$” 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 $f_{0}$, since it is known that a properly centered and normalized version of this distance is asymptotically standard normally distributed under $H_{0}$. 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
UR - http://eudml.org/doc/104269
ER -

References

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