# 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

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topDurot, 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 -

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