Marginal integration M-estimators for additive models
BOENTE, Graciela - Personal Name
MARTINEZ, Alejandra - Personal Name
Additive regression models have a long history in multivariate non-
parametric regression. They provide a model in which the regression function is
decomposed as a sum of functions, each of them depending only on a single explana-
tory variable. The advantage of additive models over general non-parametric regression
models is that they allow to obtain estimators converging at the optimal univariate rate
avoiding the so-called curse of dimensionality. Beyond backfitting, marginal integra-
tion is a common procedure to estimate each component in additive models. In this
paper, we propose a robust estimator of the additive components which combines local
polynomials on the component to be estimated with the marginal integration proce-
dure. The proposed estimators are consistent and asymptotically normally distributed.
A simulation study allows to show the advantage of the proposal over the classical one
when outliers are present in the responses, leading to estimators with good robustness
and efficiency properties.
parametric regression. They provide a model in which the regression function is
decomposed as a sum of functions, each of them depending only on a single explana-
tory variable. The advantage of additive models over general non-parametric regression
models is that they allow to obtain estimators converging at the optimal univariate rate
avoiding the so-called curse of dimensionality. Beyond backfitting, marginal integra-
tion is a common procedure to estimate each component in additive models. In this
paper, we propose a robust estimator of the additive components which combines local
polynomials on the component to be estimated with the marginal integration proce-
dure. The proposed estimators are consistent and asymptotically normally distributed.
A simulation study allows to show the advantage of the proposal over the classical one
when outliers are present in the responses, leading to estimators with good robustness
and efficiency properties.
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| EB00000004277K | Available |
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Statement of Responsibility
Graciela Boente 1, Alejandra Martínez 1
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