{$M$}-estimateurs semi-paramétriques dans les modèles à direction révélatrice unique

Delecroix, Michel; Hristache, Marian

doi:10.36045/bbms/1103141030

Cited by 13 publications

(12 citation statements)

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“…Even assuming that W is a constant, our procedure differs from the procedure used by Delecroix & Hristache (1999) and Hristache (2002) since they had a different focus, but is similar to the procedure of Delecroix et al (2003). Delecroix et al (2003) seem to prefer one-step estimation using a prior estimator other than the optimization procedure that we suggest here, which seems to perform quite well based on our limited simulations.…”

Section: Discussionmentioning

confidence: 94%

“…If both X and Y are discrete, we interpret the densities as mass functions. We now compare our procedure with a series of papers by Delecroix & Hristache (1999), Hristache (2002) and Delecroix, Härdle & Hristache (2003), which discuss a similar procedure. First, they all assume that it is sensible to make a linear combination of all the predictor variables to form a single index.…”

Section: A Search Methodsmentioning

confidence: 99%

“…Our procedure focuses on PCS. Without the single categorical variable W, although all three papers aim to estimate the single-index, Delecroix & Hristache (1999) and Hristache (2002) use additive error to restrict the single index on the mean part of the regression; that is, they focus on the central mean subspace . Our setting has no restriction on the single index at all as long as Y is related to X through this index.…”

Section: A Search Methodsmentioning

confidence: 99%

See 2 more Smart Citations

Non-Parametric Estimation of Direction in Single-Index Models With Categorical Predictors

Yin

2005

Aust NZ J Stat

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This paper proposes a general dimension-reduction method targeting the partial central subspace recently introduced by Chiaromonte, Cook & Li. The dependence need not be confined to particular conditional moments, nor are restrictions placed on the predictors that are necessary for methods like partial sliced inverse regression. The paper focuses on a partially linear single-index model. However, the underlying idea is applicable more generally. Illustrative examples are presented.

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Section: Discussionmentioning

confidence: 94%

Section: A Search Methodsmentioning

confidence: 99%

Section: A Search Methodsmentioning

confidence: 99%

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Non-Parametric Estimation of Direction in Single-Index Models With Categorical Predictors

Yin

2005

Aust NZ J Stat

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“…The theory of M-estimators was initiated by the seminal papers of Klein and Spady [26] in the case of the so-called binary response model, and Ichimura [21] for the general single-index regression model. Sherman [41] and Delecroix and Hristache [7] extended this approach. Härdle et al [18] and Delecroix et al [8] discussed the choice of the bandwidth for the nonparametric estimation of the link function.…”

Section: The M-estimate Criterionmentioning

confidence: 99%

“…Both situations are distinguished for pedagogical reasons (see the discussion about Kendall's tau below). In numerous practical situations, Assumptions (6) and (7) are simply moment-like conditions, as in the GMM methodology: there is a map g :…”

Section: Estimation Of the Link Function ψmentioning

confidence: 99%

Single-index copulas

Fermanian

Lopez

2018

Journal of Multivariate Analysis

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We introduce so-called single-index copulas. They are semi-parametric conditional copulas whose parameter is an unknown link function of a univariate index only. We propose estimates of this link function and of the finite-dimensional unknown parameter. The asymptotic properties of the latter estimates are stated. Thanks to some properties of conditional Kendall's tau, we illustrate our technical conditions with several usual copula families.

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On semiparametric -estimation in single-index regression

Delecroix

Hristache

Patilea

2006

Journal of Statistical Planning and Inference

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In this paper we analyze a large class of semiparametric M −estimators for singleindex models, including semiparametric quasi-likelihood and semiparametric maximum likelihood estimators. Some possible applications to robustness are also mentioned. The definition of these estimators involves a kernel regression estimator for which a bandwidth rule is necessary. Given the semiparametric M −estimation problem, we propose a natural bandwidth choice by joint maximization of the M −estimation criterion with respect to the parameter of interest and the bandwidth. In this way we extend a methodology first introduced by Härdle, Hall and Ichimura (1993) for semiparametric least-squares. We prove asymptotic normality for our semiparametric estimator. We derive the asymptotic equivalence between our bandwidth and the optimal bandwidth obtained through weighted cross-validation. Empirical evidence obtained from simulations suggests that our bandwidth improves the higher order asymptotics of the semiparametric M −estimator when it replaces the usual bandwidth chosen by cross-validation.

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{$M$}-estimateurs semi-paramétriques dans les modèles à direction révélatrice unique

Cited by 13 publications

References 0 publications

Non-Parametric Estimation of Direction in Single-Index Models With Categorical Predictors

Non-Parametric Estimation of Direction in Single-Index Models With Categorical Predictors

Single-index copulas

On semiparametric -estimation in single-index regression

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