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 -
References
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