Sequential design for nonparametric inference

Zhao, Zhibiao; Yao, Weixin

doi:10.1002/cjs.11128

“…The sequential design for nonparametric regression models has been less developed. Zhao & Yao (2012) discussed the sequential design problem in the context of kernel regression, based on the mean integrated square error criterion. Bull et al (2013) studied a similar problem in cases with a univariate nonparametric regression model that is esti-mated by the wavelet decomposition approach.…”

Section: Related Workmentioning

confidence: 99%

Sequential Adaptive Design for Jump Regression Estimation

Park¹,

Qiu²

2019

Preprint

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Selecting input data or design points for statistical models has been of great interest in sequential design and active learning. In this paper, we present a new strategy of selecting the design points for a regression model when the underlying regression function is discontinuous. Two main motivating examples are (1) compressed material imaging with the purpose of accelerating the imaging speed and (2) design for regression analysis over a phase diagram in chemistry. In both examples, the underlying regression functions have discontinuities, so many of the existing design optimization approaches cannot be applied for the two examples because they mostly assume a continuous regression function. There are some studies for estimating a discontinuous regression function from its noisy observations, but all noisy observations are typically provided in advance in these studies. In this paper, we develop a design strategy of selecting the design points for regression analysis with discontinuities. We first review the existing approaches relevant to design optimization and active learning for regression analysis and discuss their limitations in handling a discontinuous regression function. We then present our novel design strategy for a regression analysis with discontinuities: some statistical properties with a fixed design will be presented first, and then these properties will be used to propose a new criterion of selecting the design points for the regression analysis. Sequential design of experiments with the new criterion will be presented with numerical examples.

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“…, X n to obtain the most precise estimates of the regression function f and several authors have worked on this problem. For example, Müller (1984) and Zhao and Yao (2012) derived optimal designs with respect to different criteria for kernel estimates, while Dette and Wiens (2008) considered the design problem for series estimation in terms of spherical harmonics. We also refer to the work of Efromovich (2008), who proposed a sequential allocation scheme in a nonparametric model of the form (1.1) with random predictors and heteroscedastic errors.…”

Section: Introductionmentioning

confidence: 99%

Optimal Designs for Series Estimation in Nonparametric Regression With Correlated Data

Dette¹,

Konstantinou²,

Schorning³

2021

STAT SINICA

0

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In this paper we investigate the problem of designing experiments for series estimators in nonparametric regression models with correlated observations. We use projection based estimators to derive an explicit solution of the best linear oracle estimator in the continuous time model for all Markovian-type error processes. These solutions are then used to construct estimators, which can be calculated from the available data along with their corresponding optimal design points. Our results are illustrated by means of a simulation study, which demonstrates that the new series estimator has a better performance than the commonly used techniques based on the optimal linear unbiased estimators. Moreover, we show that the performance of the estimators proposed in this paper can be further improved by choosing the design points appropriately.

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“…, X n to obtain the most precise estimates of the regression function f and several authors have worked on this problem. For example, Müller (1984), Biedermann and Dette (2001) and Zhao and Yao (2012) derived optimal designs with respect to different criteria for kernel estimates, while Dette and Wiens (2008a) and Dette and Wiens (2008b) considered the design problem for series estimation in terms of spherical harmonics and Zernike polynomials, respectively. We also refer to the work of Efromovich (2008), who proposed a sequential allocation scheme in a nonparametric model of the form (1.1) with random predictors and heteroscedastic errors.…”

Section: Introductionmentioning

confidence: 99%

Optimal designs for series estimation in nonparametric regression with correlated data

Dette¹,

Konstantinou²,

Schorning³

2018

Preprint

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In this paper we investigate the problem of designing experiments for series estimators in nonparametric regression models with correlated observations. We use projection based estimators to derive an explicit solution of the best linear oracle estimator in the continuous time model for all Markovian-type error processes. These solutions are then used to construct estimators, which can be calculated from the available data along with their corresponding optimal design points. Our results are illustrated by means of a simulation study, which demonstrates that the new series estimator has a better performance than the commonly used techniques based on the optimal linear unbiased estimators. Moreover, we show that the performance of the estimators proposed in this paper can be further improved by choosing the design points appropriately.

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Sequential design for nonparametric inference

Cited by 6 publications

References 76 publications

Sequential Adaptive Design for Jump Regression Estimation

Sequential Adaptive Design for Jump Regression Estimation

Optimal Designs for Series Estimation in Nonparametric Regression With Correlated Data

Optimal designs for series estimation in nonparametric regression with correlated data

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