Data sharpening methods for bias reduction in nonparametric regression

Choi, Edwin; Hall, Peter; Rousson, Valentin

doi:10.1214/aos/1015957396

Cited by 39 publications

(4 citation statements)

References 14 publications

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“…The asymptotic normality of the Nadaraya-Watson estimator was proved by Schuster [34]. Moreover, Choi, Hall and Rousson [5] propose three data-sharpening versions of the Nadaraya-Watson estimator in order to reduce the asymptotic variance in the central limit theorem. Furthermore, in the situation where the regression function is monotone, Hall and Huang [14] provide a method for monotonizing the Nadaraya-Watson estimator.…”

Section: Introductionmentioning

confidence: 99%

A Robbins–Monro procedure for estimation in semiparametric regression models

Bercu¹,

Fraysse²

2012

Ann. Statist.

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This paper is devoted to the parametric estimation of a shift together with the nonparametric estimation of a regression function in a semiparametric regression model. We implement a very efficient and easy to handle Robbins-Monro procedure. On the one hand, we propose a stochastic algorithm similar to that of Robbins-Monro in order to estimate the shift parameter. A preliminary evaluation of the regression function is not necessary to estimate the shift parameter. On the other hand, we make use of a recursive Nadaraya-Watson estimator for the estimation of the regression function. This kernel estimator takes into account the previous estimation of the shift parameter. We establish the almost sure convergence for both Robbins-Monro and Nadaraya-Watson estimators. The asymptotic normality of our estimates is also provided. Finally, we illustrate our semiparametric estimation procedure on simulated and real data.

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Section: Introductionmentioning

confidence: 99%

A Robbins–Monro procedure for estimation in semiparametric regression models

Bercu¹,

Fraysse²

2012

Ann. Statist.

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“…Some interest on density estimation research is on bias reduction techniques, which can be found in Jones, Linton and Nielsen (1995), Choi and Hall (1999), Cheng, Choi, Fan and Hall (2000), Choi, Hall and Roussan (2000) and Hall and Minnotte (2002). Other recent improvements and interesting applications of the kernel estimate can be found in Hirukawa (2010), Liao, Wu and Lin (2010), Matuszyk, Cardew-Hall and Rolfe (2010), Miao, Rahimi and Rao (2012), Chu, Liau, Lin and Su (2012), Golyandina, Pepelyshev and Steland (2012) and Cai, Rushton and Bhaduri (2012) among many others.…”

Section: Estimating Densities On R +mentioning

confidence: 99%

A Review of Kernel Density Estimation with Applications to Econometrics

Zambom¹,

Dias²

2012

Preprint

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Nonparametric density estimation is of great importance when econometricians want to model the probabilistic or stochastic structure of a data set. This comprehensive review summarizes the most important theoretical aspects of kernel density estimation and provides an extensive description of classical and modern data analytic methods to compute the smoothing parameter. Throughout the text, several references can be found to the most up-to-date and cut point research approaches in this area, while econometric data sets are analyzed as examples. Lastly, we present SIZer, a new approach introduced by Chaudhuri and Marron (2000), whose objective is to analyze the visible features representing important underlying structures for different bandwidths.

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“…The idea of estimating the bias from residuals to correct a pilot estimator of a regression function goes back to the concept of twicing introduced by Tukey [1977] to estimate bias of misspecified multivariate regression models. Numerous authors have shown the benefits of various bias reduction techniques in nonparametric regression, including He and Huang [2009], Choi et al [2000], Choi and Hall [1998], Hengartner et al [2010], Hirukawa [2010].…”

Section: Introductionmentioning

confidence: 99%

Recursive bias estimation for multivariate regression smoothers

2014

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This paper presents a practical and simple fully nonparametric multivariate smoothing procedure that adapts to the underlying smoothness of the true regression function. Our estimator is easily computed by successive application of existing base smoothers (without the need of selecting an optimal smoothing parameter), such as thin-plate spline or kernel smoothers. The resulting smoother has better out of sample predictive capabilities than the underlying base smoother, or competing structurally constrained models (GAM) for small dimension (3 ≤ d ≤ 7) and moderate sample size n ≤ 800. Moreover our estimator is still useful when d > 10 and to our knowledge, no other adaptive fully nonparametric regression estimator is available without constrained assumption such as additivity for example. On a real example, the Boston Housing Data, our method reduces the out of sample prediction error by 20%. An R package ibr, available at CRAN, implements the proposed multivariate nonparametric method in R.AMS 2000 subject classifications: 62G08.

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Data sharpening methods for bias reduction in nonparametric regression

Cited by 39 publications

References 14 publications

A Robbins–Monro procedure for estimation in semiparametric regression models

A Robbins–Monro procedure for estimation in semiparametric regression models

A Review of Kernel Density Estimation with Applications to Econometrics

Recursive bias estimation for multivariate regression smoothers

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