An optimal experimental design for the haar regression model

Herzberg, Agnes M.; Traves, William N.

doi:10.2307/3315597

Cited by 23 publications

(14 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is worthwhile to mention that this conclusion is always possible, provided that z (x) is constant. Popular examples satisfying this property are the Haar wavelet model [see Herzberg and Traves (1994) and Oyet and Wiens (2000)] and the trigonometric regression model [see Karlin and Studden (1966)]. …”

Section: Moreover the Matrix K M − B 2 M Is Non-negative Definite; Imentioning

confidence: 99%

“…Lau and Studden (1985), Herzberg and Traves (1994) and Dette, Melas and Pepelyshev (2005) among others]. Recently, Dette, Melas and Pepelyshev (2007) investigated optimal designs minimizing the generalized variance of the least squares and direct estimates of the parameters in truncated Fourier expansions resulting from the system of Zernike polynomials.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust designs for series estimation

Dette

Wiens

2008

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

We discuss optimal design problems for a popular method of series estimation in regression problems. Commonly used design criteria are based on the generalized variance of the estimates of the coefficients in a truncated series expansion and do not take possible bias into account. We present a general perspective of constructing robust and efficient designs for series estimators which is based on the integrated mean squared error criterion. A minimax approach is used to derive designs which are robust with respect to deviations caused by the bias and the possibility of heteroscedasticity. A special case results from the imposition of an unbiasedness constraint; the resulting "unbiased designs" are particularly simple, and easily implemented. Our results are illustrated by constructing robust designs for series estimation with spherical harmonic descriptors, Zernike polynomials and Chebyshev polynomials.

show abstract

Section: Moreover the Matrix K M − B 2 M Is Non-negative Definite; Imentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust designs for series estimation

Dette

Wiens

2008

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

show abstract

“…Some efficient designs for certain specific wavelet regression models have been investigated by Herzberg and Traves [8], Xie [9], and Tian and Herzberg [10], among others. Herzberg and Traves [8] discussed D-optimal designs for the Haar wavelet model and Xie [9] provided the D-optimal designs for b-adic Haar wavelet models; more recently, Tian and Herzberg [10] constructed D-optimal designs for a combined linear and Haar wavelet function.…”

Section: Introductionmentioning

confidence: 99%

Robust designs for Haar wavelet approximation models

Zhao

2010

Appl Stoch Models Bus & Ind

View full text Add to dashboard Cite

In this paper, we discuss the construction of robust designs for heteroscedastic wavelet regression models when the assumed models are possibly contaminated over two different neighbourhoods: G 1 and G 2 . Our main findings are: (1) A recursive formula for constructing D-optimal designs under G 1 ; (2) Equivalency of Q-optimal and A-optimal designs under both G 1 and G 2 ; (3) D-optimal robust designs under G 2 ; and (4) Analytic forms for A-and Q-optimal robust design densities under G 2 . Several examples are given for the comparison, and the results demonstrate that our designs are efficient.

show abstract

“…See for instance, Box and Draper (1959) or Wiens (1992) for developments of these notions in general regression models. Particular applications to wavelet models have been studied by Herzberg and Traves (1994), Xie (1998), Oyet and Wiens (2000) and Oyet (2002).…”

Section: Introductionmentioning

confidence: 99%