On bias reduction in local linear smoothing

Choi, Edwin; Hall, Peter

doi:10.1093/biomet/85.2.333

Cited by 33 publications

(25 citation statements)

References 11 publications

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“…x W x Z x G is asymptotically a block diagonal matrix; that is, there exist two matrices L 11 and L 22 such…”

Section: Estimators To Be Plugged Inmentioning

confidence: 99%

“…Some versions of DS methods have been discussed in a series of works by Choi and Hall [11,12]. It is well known that the bias of the LL estimator is second order, which is the same as the order of the kernel utilized ( [1], Section 2.8), while DS estimators in [10] have fourth order bias even though the kernel utilized is only of second order.…”

Section: Introductionmentioning

confidence: 99%

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Bandwidth selection for a data sharpening estimator in nonparametric regression

Naito

Yoshizaki

2009

Journal of Multivariate Analysis

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a b s t r a c tThis paper is concerned with data-based selection of the bandwidth for a data sharpening estimator in nonparametric regression. Two kinds of bandwidths are considered: a bandwidth vector which has a different bandwidth for each covariate, and a scalar bandwidth that is common for all covariates. A plug-in method is developed and its theoretical performance is fully investigated. The proposed plug-in method works efficiently in our simulation study.

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“…x W x Z x G is asymptotically a block diagonal matrix; that is, there exist two matrices L 11 and L 22 such…”

Section: Estimators To Be Plugged Inmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bandwidth selection for a data sharpening estimator in nonparametric regression

Naito

Yoshizaki

2009

Journal of Multivariate Analysis

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“…The other approach is to use information of those closest design points and the idea of the model average to find an approximately unbias estimate (see Choi and Hall, 1998, Choi, Hall and Rousson, 2000, He and Huang,2009. For the first approach, the computational burden is very heavy.…”

Section: Introductionmentioning

confidence: 99%

Bias Reduction for Nonparametric and Semiparametric Regression Models

Cheng¹,

Huang

Liu

et al. 2018

STAT SINICA

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Abstract:Nonparametric and semiparametric regression models are useful statistical regression models to discover nonlinear relationships between the response variable and predictor variables. However, optimal efficient estimates for the nonparametric components in the models are biased which hinders the development of methods for further statistical inference. In this paper, based on the local linear fitting, we propose a simple bias reduction approach for the estimation of the nonparametric regression model. The new approach does not need to use higher-order local polynomial regression to estimate the bias, and hence avoids the double bandwidth selection and the design sparsity problems suffered by higher-order local polynomial fitting. It also does not inflate the variance. Hence it can be easily applied to complex statistical inference problems. We extend our new approach Statistica Sinica: Newly accepted Paper (accepted version subject to English editing)to varying coefficient models, and to estimate the variance function and to construct simultaneous confidence band for the nonparametric regression function.Simulations are carried out for comparisons with existing methods, and a real data example is used to investigate the performance of the proposed method.

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“…To correct this problem, Nishida and Kanazawa (2015) proposed a variance-stabilizing (VS) local variable bandwidth for Local Linear (LL) regression estimator. In contrast, Choi and Hall (1998) proposed the skewing (SK) methods for a univariate LL estimator and constructed a convex combination of one LL estimator and two SK estimators that are symmetrically placed on both sides of the LL estimator (the convex combination (CC) estimator) to eliminate higher-order terms in its asymptotic bias. To obtain a CC estimator with a constant estimator variance without employing the VS local variable bandwidth, the weight in the convex combination must be determined locally to produce a constant estimator variance.…”

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confidence: 99%

Skewing methods for variance-stabilizing local linear regression estimation

Nishida

2019

Communications in Statistics - Simulation and Computation

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It is well-known that kernel regression estimators do not produce a constant estimator variance over a domain. To correct this problem, Nishida and Kanazawa (2015) proposed a variance-stabilizing (VS) local variable bandwidth for Local Linear (LL) regression estimator. In contrast, Choi and Hall (1998) proposed the skewing (SK) methods for a univariate LL estimator and constructed a convex combination of one LL estimator and two SK estimators that are symmetrically placed on both sides of the LL estimator (the convex combination (CC) estimator) to eliminate higher-order terms in its asymptotic bias. To obtain a CC estimator with a constant estimator variance without employing the VS local variable bandwidth, the weight in the convex combination must be determined locally to produce a constant estimator variance. In this study, we compare the performances of two VS methods for a CC estimator and find cases in which the weighting method can superior to the VS bandwidth method in terms of the degree of variance stabilization.

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On bias reduction in local linear smoothing

Cited by 33 publications

References 11 publications

Bandwidth selection for a data sharpening estimator in nonparametric regression

Bandwidth selection for a data sharpening estimator in nonparametric regression

Bias Reduction for Nonparametric and Semiparametric Regression Models

Skewing methods for variance-stabilizing local linear regression estimation

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