Multivariate Locally Weighted Least Squares Regression

Ruppert, David; Wand, M. P.

doi:10.1214/aos/1176325632

Cited by 885 publications

(600 citation statements)

References 19 publications

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“…From this proof we can see that if m is a linear functional then the local linear estimator is unbiased. This fact was already observed by Fan (1992) and Ruppert and Wand (1994) in the case that X has finite dimension.…”

Section: Asymptotic Behavioursupporting

confidence: 67%

Local Linear Regression for Functional Predictor and Scalar Response

Grané

Baı́llo

2008

Contributions to Statistics

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The aim of this work is to introduce a new nonparametric regression technique in the context of functional covariate and scalar response. We propose a local linear regression estimator and study its asymptotic behaviour. Its finite-sample performance is compared with a Nadayara-Watson type kernel regression estimator via a Monte Carlo study and the analysis of two real data sets. In all the scenarios considered, the local linear regression estimator performs better than the kernel one, in the sense that the mean squared prediction error and its standard deviation are lower. Keywords AbstractThe aim of this work is to introduce a new nonparametric regression technique in the context of functional covariate and scalar response. We propose a local linear regression estimator and study its asymptotic behaviour. Its finite-sample performance is compared with a Nadayara-Watson type kernel regression estimator via a Monte Carlo study and the analysis of two real data sets. In all the scenarios considered, the local linear regression estimator performs better than the kernel one, in the sense that the mean squared prediction error and its standard deviation are lower.

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Section: Asymptotic Behavioursupporting

confidence: 67%

Local Linear Regression for Functional Predictor and Scalar Response

Grané

Baı́llo

2008

Contributions to Statistics

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“…Our algorithm is based on local linear regression [13,5]. Sensor readings from static nodes (a set of buoys) are sent to the mobile robot (a boat) and used to estimate the Hessian Matrix of the scalar field (the surface temperature of a lake), which is directly related to the estimation error.…”

Section: Contributionsmentioning

confidence: 99%

AMBROSia: An Autonomous Model-Based Reactive Observing System

Caron

Das

Dhariwal

et al. 2007

Computational Science – ICCS 2007

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Abstract. Observing systems facilitate scientific studies by instrumenting the real world and collecting corresponding measurements, with the aim of detecting and tracking phenomena of interest. Our AMBROSia project focuses on a class of observing systems which are embedded into the environment, consist of stationary and mobile sensors, and react to collected observations by reconfiguring the system and adapting which observations are collected next. In this paper, we report on recent research directions and corresponding results in the context of AMBROSia.

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“…Again the monotonized estimate is first order equivalent to the unconstrained local linear estimate [see e.g. Ruppert and Wand (1994)]. Because of its better performance at the boundary, the local linear estimate was in fact used in our numerical examples, which will be described in the following section.…”

Section: Asymptotic Theorymentioning

confidence: 99%

“…In order to avoid boundary effects, we implemented the new procedure using a two dimensional local linear estimator [see Ruppert and Wand (1994)] and the bandwidth h r,1 = h r,2 = σ 2 n 1/6 (4.1) whereσ 2 = σ 2 (u, v)dudv denotes the integrated variance and n is the sample size. For the kernel K r , we used a product kernel based on two Epanechnikov kernels k(x) = 3 4 (1 − x 2 )I [−1,1] (x) and the same kernel was used for K d in step 1 and 3 of the procedure.…”

Section: A Small Simulation Studymentioning

confidence: 99%

Strictly monotone and smooth nonparametric regression for two or more variables

Dette

Scheder

2006

Can J Statistics

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In this article a new monotone nonparametric estimate for a regression function of two or more variables is proposed. The method starts with an unconstrained nonparametric regression estimate and uses successively one-dimensional isotonization procedures. In the case of a strictly monotone regression function, it is shown that the new estimate is first order asymptotic equivalent to the unconstrained estimate, and asymptotic normality of an appropriate standardization of the estimate is established. Moreover, if the regression function is not monotone in one of its arguments, the constructed estimate has approximately the same L p -norm as the initial unconstrained estimate. The methodology is also illustrated by means of a simulation study, and two data examples are analyzed.

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Multivariate Locally Weighted Least Squares Regression

Cited by 885 publications

References 19 publications

Local Linear Regression for Functional Predictor and Scalar Response

Local Linear Regression for Functional Predictor and Scalar Response

AMBROSia: An Autonomous Model-Based Reactive Observing System

Strictly monotone and smooth nonparametric regression for two or more variables

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