Indicator function based on complex contrasts and its application in general factorial designs

Pang, Fang; Liu, Min-Qian

doi:10.1016/j.jspi.2009.07.002

Cited by 10 publications

(4 citation statements)

References 11 publications

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“…The approach for qualitative factors taken by Evangelaras et al is unreasonable, as will be demonstrated in Example 5. Pang and Liu (2010) also proposed a generalized resolution based on complex contrasts. For designs with more than 3 levels, permuting levels for one or more factors will lead to different generalized resolutions according to their definition, which is unacceptable for qualitative factors.…”

Section: Generalized Resolution For Orthogonal Arraysmentioning

confidence: 99%

“…Using this example, we now compare the GR introduced here to proposals by Evangelaras et al (2005) and Pang and Liu (2010): The GRes values reported by Evangelaras et al (2005) for designs D 1 , D 2 and D 3 in the qualitative case are 3.75, 3.6464, 3.5, respectively; especially the 3.5 for the completely aliased design D 3 does not make sense. Pang and Liu reported values 3.75, 3.75 and 3, respectively; here, at least the completely aliased design D 3 is assigned the value "3."…”

Section: Rowmentioning

confidence: 99%

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Generalized resolution for orthogonal arrays

Grömping¹,

Xu²

2014

Ann. Statist.

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The generalized word length pattern of an orthogonal array allows a ranking of orthogonal arrays in terms of the generalized minimum aberration criterion (Xu and Wu [Ann. Statist. 29 (2001) 1066-1077]). We provide a statistical interpretation for the number of shortest words of an orthogonal array in terms of sums of $R^2$ values (based on orthogonal coding) or sums of squared canonical correlations (based on arbitrary coding). Directly related to these results, we derive two versions of generalized resolution for qualitative factors, both of which are generalizations of the generalized resolution by Deng and Tang [Statist. Sinica 9 (1999) 1071-1082] and Tang and Deng [Ann. Statist. 27 (1999) 1914-1926]. We provide a sufficient condition for one of these to attain its upper bound, and we provide explicit upper bounds for two classes of symmetric designs. Factor-wise generalized resolution values provide useful additional detail.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1205 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

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Section: Generalized Resolution For Orthogonal Arraysmentioning

confidence: 99%

Section: Rowmentioning

confidence: 99%

Generalized resolution for orthogonal arrays

Grömping¹,

Xu²

2014

Ann. Statist.

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“…Some other criteria are also proposed in literature, such as the minimum generalized aberration (see Ma and Fang [7]), the general minimum lower order confounding (see Zhang et al. [14]) and the minimum hybrid aberration (Pang and Liu [9]). More discussions about the criteria for designs with qualitative factors can be found in Mukerjee and Wu [8], Wu and Hamada [12] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Some properties of β-wordlength pattern for four-level designs

Sheng

Tang

2015

Acta. Math. Sin.-English Ser.

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Fractional factorial designs have played a prominent role in the theory and practice of experimental design. For designs with qualitative factors under an ANOVA model, the minimum aberration criterion has been frequently used; however, for designs with quantitative factors, a polynomial regression model is often established, thus the β-wordlength pattern can be employed to compare different fractional factorial designs. Although the β-wordlength pattern was introduced in 2004, its properties have not been investigated extensively. In this paper, we will present some properties of β-wordlength pattern for four-level designs. These properties can help find better designs with quantitative factors.

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“…[15][16][17] For dealing with the multicomponent mixture systems, the first step is usually the determination of the number of ranks, or absorptive chemical components (ACCs), factors, principal components (PCs), and independent components (ICs), etc., in the mixtures. [18][19][20][21][22][23][24][25][26] Compared with empirical methods 19,20,[27][28][29][30] and pseudo-statistical methods, 21,22,25,31,32 statistical methods are based on well-established statistical principles and are free from questionable assumptions. 23,[33][34][35] The median absolute deviation (MAD) 35 is employed as a simple non-parametric statistical evaluation criterion with excellent robustness, 26,36 and it therefore was used for determination of the number of ACCs/ICs in the AKICA algorithm proposed here.…”

Section: Introductionmentioning

confidence: 99%

Adaptive kernel independent component analysis and UV spectrometry applied to characterize the procedure for processing prepared rhubarb roots

Wang

Hou

Yang

et al. 2011

Analyst

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By determination of the number of absorptive chemical components (ACCs) in mixtures using median absolute deviation (MAD) analysis and extraction of spectral profiles of ACCs using kernel independent component analysis (KICA), an adaptive KICA (AKICA) algorithm was proposed. The proposed AKICA algorithm was used to characterize the procedure for processing prepared rhubarb roots by resolution of the measured mixed raw UV spectra of the rhubarb samples that were collected at different steaming intervals. The results show that the spectral features of ACCs in the mixtures can be directly estimated without chemical and physical pre-separation and other prior information. The estimated three independent components (ICs) represent different chemical components in the mixtures, which are mainly polysaccharides (IC1), tannin (IC2), and anthraquinone glycosides (IC3). The variations of the relative concentrations of the ICs can account for the chemical and physical changes during the processing procedure: IC1 increases significantly before the first 5 h, and is nearly invariant after 6 h; IC2 has no significant changes or is slightly decreased during the processing procedure; IC3 decreases significantly before the first 5 h and decreases slightly after 6 h. The changes of IC1 can explain why the colour became black and darkened during the processing procedure, and the changes of IC3 can explain why the processing procedure can reduce the bitter and dry taste of the rhubarb roots. The endpoint of the processing procedure can be determined as 5-6 h, when the increasing or decreasing trends of the estimated ICs are insignificant. The AKICA-UV method provides an alternative approach for the characterization of the processing procedure of rhubarb roots preparation, and provides a novel way for determination of the endpoint of the traditional Chinese medicine (TCM) processing procedure by inspection of the change trends of the ICs.

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Indicator function based on complex contrasts and its application in general factorial designs

Cited by 10 publications

References 11 publications

Generalized resolution for orthogonal arrays

Generalized resolution for orthogonal arrays

Some properties of β-wordlength pattern for four-level designs

Adaptive kernel independent component analysis and UV spectrometry applied to characterize the procedure for processing prepared rhubarb roots

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