# 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

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topDurot, 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 -

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