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[GSY10] On semiparametric mode regression estimation
Revue Internationale avec comité de lecture : Journal Communications in Statistics - Theory and Methods, vol. 39(7), pp. 1141-1157, 2010
motcle:
Résumé:
It has been found that, for a variety of probability distributions, there is
a surprising linear relation between mode, mean and median.
In this paper, the relation between mode, mean and median
regression functions is assumed to follow a simple parametric
model. We propose a semiparametric conditional mode (mode
regression) estimation for an unknown (unimodal) conditional
distribution function in the context of regression model, so that any $m$-step-ahead mean and median forecasts
can then be substituted into the resultant model to deliver $m$-step-ahead mode prediction.
In the semiparametric model,
Least Squared Estimator (LSEs)
for the model parameters
and the simultaneous estimation of the unknown mean
and median regression functions by the local linear kernel method
are combined to infer about the parametric and nonparametric components
of the proposed model. The asymptotic normality of these
estimators is derived, and the asymptotic distribution of the
parameter estimates is also given and is shown to follow usual
parametric rates in spite of the presence of the nonparametric
component in the model. These results are applied to obtain a
data-based test for the dependence of mode regression over mean
and median regression under a regression model.
Equipe:
msdma
BibTeX
| @article { | |||
| GSY10, | |||
| title | = | "{On semiparametric mode regression estimation}", | |
| author | = | "A. Gannoun and A. Saracco and K. Yu", | |
| journal | = | "Communications in Statistics - Theory and Methods", | |
| year | = | 2010, | |
| volume | = | 39, | |
| number | = | 7, | |
| pages | = | "1141-1157", | |
| } | |||
