Sequential design for response curve estimation

Park, Dongryeon; Faraway, Julian J.

doi:10.1080/10485259808832740

Cited by 5 publications

(4 citation statements)

References 6 publications

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“…In particular, we use the optimal designs to demonstrate that in many cases the popular uniform allocation is extremely efficient with respect to the integrated MSE criterion. Moreover, the optimal designs determined in this section can be used in more advanced sequential design procedures as considered by Park (2000), Park and Faraway (1998) or Efromovich (2008) in the case of direct nonparametric regression.…”

Section: Optimal Designsmentioning

confidence: 99%

“…Moreover, the optimal designs determined in this section can be used in more advanced sequential design procedures as considered by Park (2000); Park and Faraway (1998) or Efromovich (2008) in the case of direct nonparametric regression. While for fixed m and σ 2 the optimal design density can be found explicitly, the parameter of regularization usually has to be determined numerically from experimental data.…”

Section: Optimal Designsmentioning

confidence: 99%

“…Designs minimizing the integrated mean squared error of a nonparametric estimate in direct regression models have been investigated by Mueller (1984) and Cheng et al (1998) among others, while Chan (1992) considered optimal designs for variance estimation. More recent work discussed the construction of sequential optimal designs in this context [see Park (2000); Park and Faraway (1998) or Efromovich (2008)]. …”

Section: Introductionmentioning

confidence: 99%

“…These designs serve as benchmarks for commonly used designs in indirect regression. Moreover they can be used in more advanced sequential design procedures as considered by Park (2000); Park and Faraway (1998) or Efromovich (2008) in the case of direct nonparametric regression. In this paper we worked in the first named direction and investigated the efficiency of the uniform design in several situations of practical interest.…”

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confidence: 99%

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Optimal designs for indirect regression

Biedermann¹,

Bissantz²,

Dette³

et al. 2011

Inverse Problems

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In many real life applications, it is impossible to observe the feature of interest directly. For example, scientists in Materials Science may be interested in detecting cracks inside objects, not visible from the outside. Similarly, non-invasive medical imaging techniques such as Positrone Emission Tomography rely on indirect observations to reconstruct an image of the patient's internal organs. In this paper, we investigate optimal designs for such indirect regression problems. We determine designs minimizing the integrated mean squared error of estimates of the regression function obtained by Tikhonov or spectral cut-off regularization. We use the optimal designs as benchmarks to investigate the efficiency of the uniform design commonly used in applications. Several examples are discussed to illustrate the results, in most of which the uniform design or a simple modification thereof is demonstrated to be very efficient for the estimation of the regression function. Our designs provide guidelines to scientists regarding the experimental conditions at which the indirect observations should be taken in order to obtain an accurate estimate for the object of interest.

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Section: Optimal Designsmentioning

confidence: 99%

Section: Optimal Designsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Optimal designs for indirect regression

Biedermann¹,

Bissantz²,

Dette³

et al. 2011

Inverse Problems

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Sequential design for nonparametric inference

Zhao

Yao

2012

Can J Statistics

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The performance of nonparametric function estimates often depends on the choice of design points. Based on the mean integrated squared error criterion, we propose a sequential design procedure that updates the model knowledge and optimal design density sequentially. The methodology is developed under a general framework covering a wide range of nonparametric inference problems, such as conditional mean and variance functions, the conditional distribution function, the conditional quantile function in quantile regression, functional coefficients in varying coefficient models and semiparametric inferences. Based on our empirical studies, nonparametric inference based on the proposed sequential design is more efficient than the uniform design and its performance is close to the true but unknown optimal design. The Canadian Journal of Statistics 40: 362–377; 2012 © 2012 Statistical Society of Canada

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Sequential design for local bandwidth response curve estimator

Park¹

2000

Journal of Nonparametric Statistics

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Sequential design for response curve estimation

Cited by 5 publications

References 6 publications

Optimal designs for indirect regression

Optimal designs for indirect regression

Sequential design for nonparametric inference

Sequential design for local bandwidth response curve estimator

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