Bandwidth Choice for Average Derivative Estimation

Härdle, Wolfgang Karl; Hart, Jeffrey D.; Marron, J. S.; Tsybakov, Alexandre B.

doi:10.2307/2290472

Cited by 29 publications

(15 citation statements)

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“…First, it avoids the estimation of the link function; and second, it achieves the root-n convergence rate. See [10][11][12] for more discussions. The main drawback of ADE is that it can only recover one direction.…”

Section: Introductionmentioning

confidence: 99%

An integral transform method for estimating the central mean and central subspaces

Zeng

Zhu

2010

Journal of Multivariate Analysis

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a b s t r a c tThe central mean and central subspaces of generalized multiple index model are the main inference targets of sufficient dimension reduction in regression. In this article, we propose an integral transform (ITM) method for estimating these two subspaces. Applying the ITM method, estimates are derived, separately, for two scenarios: (i) No distributional assumptions are imposed on the predictors, and (ii) the predictors are assumed to follow an elliptically contoured distribution. These estimates are shown to be asymptotically normal with the usual root-n convergence rate. The ITM method is different from other existing methods in that it avoids estimation of the unknown link function between the response and the predictors and it does not rely on distributional assumptions of the predictors under scenario (i) mentioned above.

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Section: Introductionmentioning

confidence: 99%

An integral transform method for estimating the central mean and central subspaces

Zeng

Zhu

2010

Journal of Multivariate Analysis

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“…G (x) to denote the estimator of m (1) (x) obtained from (12). Sinceˆ n,G,1 is a d × 1 vector that estimates hm (1) …”

Section: Local Polynomial Regression For Estimating Average Derivativesmentioning

confidence: 99%

“…It has an attractive feature as in linear models, because the coefficients measure the relative impacts of the individual predictor variables on the response variable. For the nonparametric regression function estimation and the average derivative technique and its economic applications, we refer the reader to Eubank [4], Härdle [10], Rilstone [30], Stoker [34], Härdle et al [12], Newey and Stoker [26] and Pagan and Ullah [27]. Estimation of point-wise derivative of the kernel regression is discussed in [8,31] among others.…”

Section: Introductionmentioning

confidence: 99%

“…Estimation of point-wise derivative of the kernel regression is discussed in [8,31] among others. Härdle and Stoker [13], Powell et al [29], Rilstone [30], Härdle et al [12], Newey and Stoker [26] have proposed √ n-consistent average derivative estimators based on Nadaraya-Watson [25,37] kernel regression estimators. In particular, the method presented in [13] is called average derivative estimation (ADE).…”

Section: Introductionmentioning

confidence: 99%

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Censored multiple regression by the method of average derivatives

Burke

2005

Journal of Multivariate Analysis

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This paper proposes a technique [termed censored average derivative estimation (CADE)] for studying estimation of the unknown regression function in nonparametric censored regression models with randomly censored samples. The CADE procedure involves three stages: firstly-transform the censored data into synthetic data or pseudo-responses using the inverse probability censoring weighted (IPCW) technique, secondly estimate the average derivatives of the regression function, and finally approximate the unknown regression function by an estimator of univariate regression using techniques for one-dimensional nonparametric censored regression. The CADE provides an easily implemented methodology for modelling the association between the response and a set of predictor variables when data are randomly censored. It also provides a technique for "dimension reduction" in nonparametric censored regression models. The average derivative estimator is shown to be root-n consistent and asymptotically normal. The estimator of the unknown regression function is a local linear kernel regression estimator and is shown to converge at the optimal one-dimensional nonparametric rate. Monte Carlo experiments show that the proposed estimators work quite well.

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“…As the required amount of undersmoothing is a sample-size-dependent quantity, this informal method does not provide much guidance and may lead to a nonnegligible bias. The derivation and application of formal data-driven bandwidth selection rules in semiparametric settings is rarely done, as it involves technical higher-order asymptotic analyses (see, for instance, Ha¨rdle et al, 1992;Hall and Horowitz, 1990) that must be rederived for each semiparametric estimator of interest, and may depend strongly on the unknown precise degree of smoothness of the estimand.…”

Section: Introductionmentioning

confidence: 99%