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Analysis of supersaturated designs via the Dantzig selector

Frederick Kin Hing Phoa, +2 more
- 01 Jul 2009 - 
- Vol. 139, Iss: 7, pp 2362-2372
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TLDR
In this article, a variable selection method via the Dantzig selector, proposed by Candes and Tao [2007], is studied and compared to existing methods in the literature and is more efficient at estimating the model size.
About: 
This article is published in Journal of Statistical Planning and Inference.The article was published on 2009-07-01 and is currently open access. It has received 92 citations till now. The article focuses on the topics: Feature selection & Akaike information criterion.

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Managing computational complexity using surrogate models: a critical review

Reza Alizadeh, +2 more
- 06 Apr 2020 - 
TL;DR: A qualitative evaluation and a mental model is proposed which is based on quantitative results and findings of authors in the published literature to provide practical guide for researchers and practitioners in industry to choose the most appropriate surrogate model based on incomplete information about an engineering design problem.
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A comparison of design and model selection methods for supersaturated experiments

Christopher J. Marley, +1 more
- 01 Dec 2010 - 
TL;DR: Simulated experiments are used to evaluate the use of E(s^2)-optimal and Bayesian D-optimal designs and to compare three analysis strategies representing regression, shrinkage and a novel model-averaging procedure.
Journal ArticleDOI

Recent developments in nonregular fractional factorial designs

Hongquan Xu, +2 more
- 01 Jan 2009 - 
TL;DR: Important developments in optimality criteria and comparison are reviewed, including projection properties, generalized resolution, various generalized minimum aberration criteria, optimality results, construction methods and analysis strategies for nonregular designs.
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A Statistical Approach to Determine Optimal Models for IUPAC-Classified Adsorption Isotherms

Md. Matiar Rahman, +6 more
- 29 Nov 2019 - 
TL;DR: In this article, the optimal models for all eight types of isotherms employing several useful statistical approaches such as average error; confidence interval (CI), information criterion (ICs), and proportion tests using bootstrap sampling were presented.
Journal ArticleDOI

Supersaturated designs: A review of their construction and analysis

Stelios Georgiou
- 01 Jan 2014 - 
TL;DR: Supersaturated designs are fractional factorial designs in which the run size (n) is too small to estimate all the main effects under the effect sparsity assumption, the use of supersaturated design can provide the low-cost identification of the few, possibly dominating factors as mentioned in this paper.
References
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Journal ArticleDOI

Regression and time series model selection in small samples

Clifford M. Hurvich, +1 more
- 01 Jun 1989 - 
TL;DR: In this article, a bias correction to the Akaike information criterion, called AICC, is derived for regression and autoregressive time series models, which is of particular use when the sample size is small, or when the number of fitted parameters is a moderate to large fraction of the sample sample size.
Journal ArticleDOI

The Dantzig selector: Statistical estimation when p is much larger than n

Emmanuel J. Candès, +1 more
- 01 Dec 2007 - 
TL;DR: In many important statistical applications, the number of variables or parameters p is much larger than the total number of observations n as discussed by the authors, and it is possible to estimate β reliably based on the noisy data y.
Journal ArticleDOI

Ridge Regression: Applications to Nonorthogonal Problems

Arthur E. Hoerl, +1 more
- 01 Feb 1970 - 
TL;DR: In this paper, the use of ridge regression methods is discussed and recommendations are made for obtaining a better regression equation than that given by ordinary least squares estimation. But the authors focus on the RIDGE TRACE which is a two-dimensional graphical procedure for portraying the complex relationships in multifactor data.
Journal ArticleDOI

A Statistical View of Some Chemometrics Regression Tools

lldiko E. Frank, +1 more
- 01 May 1993 - 
TL;DR: In this article, the authors examined partial least squares and principal components regression from a statistical perspective and compared them with other statistical methods intended for those situations, such as variable subset selection and ridge regression.
Book

Experiments: Planning, Analysis, and Parameter Design Optimization

C. F. Jeff Wu, +1 more
TL;DR: This book discusses Factorial and Fractional Factorial Experiments at Three Levels, Robust Parameter Design for Signal-Response Systems, and other Design and Analysis Techniques for Experiments for Improving Reliability.
Related Papers (5)

A new class of supersaturated designs

Dennis K.J. Lin
- 01 Feb 1993 - 

Construction of supersaturated designs through partially aliased interactions

Chien-Fu Wu
- 01 Sep 1993 - 

Some Systematic Supersaturated Designs

Kathleen H.V. Booth, +1 more
- 01 Nov 1962 - 

The Dantzig selector: Statistical estimation when p is much larger than n

Emmanuel J. Candès, +1 more
- 01 Dec 2007 - 

A Bayesian variable-selection approach for analyzing designed experiments with complex aliasing

Hugh A. Chipman, +2 more
- 01 Nov 1997 - 
Frequently Asked Questions (13)
Q1. What are the contributions mentioned in the paper "Analysis of supersaturated designs via the dantzig selector" ?

In this paper, the authors study a variable selection method via the Dantzig selector, proposed by Candes and Tao ( 2007 ), to screen important effects. A graphical procedure and an automated procedure are suggested to accompany with the method. 

The authors run the simulations 1,000 times by fixing γ = 1 (corresponding to 10% or 6.7% of max |βi|) and choosing δ automatically using mAIC. 

Linear programming algorithms are available in many software and packages, like R, Matlab, Mathematica, etc., making it easy to program and use the Dantzig selector. 

The Dantzig selector chooses the best subset of variables or active factors by solving a simple convex program, which can be recast as a convenient linear program. 

As science and technology have advanced to a higher level nowadays, investigators are becoming more interested in and capable of studying large-scale systems. 

The Dantzig selector method is very effective in identifying 1 active factor; the TIMR ranges from 96% to 100% and the average model size ranges from 1 to 1.04. 

Candes and Tao (2007) suggested the choice of δ = λσ when X is unit length normalized, where λ = √ 2 log k and σ is the standard deviation of the random error. 

Candes and Tao (2007) showed that the Dantzig selector has some remarkable properties under some conditions and has been successfully used in biomedical imaging, analog to digital conversion and sensor networks, where the goals are to recover some sparse signals from some massive data. 

The former suggested the use of random balanced designs and the latter proposed an algorithm to construct systematic supersaturated designs. 

the authors rely on the Dantzig selector to estimate the model The authorby Î, and construct a new estimator by regressing y onto the model Î. Candes and Tao (2007) referred to this estimator as the Gauss-Dantzig selector. 

Note that the significance of AE without its parent main effects violates the effect heredity principle (Wu and Hamada 2000, section 3.5), so one might accept a model with F and FG only, which is recommended by Wu and Hamada (2000, Section 8.4). 

For each model, the authors generate data 100 times according model (5) and obtain the true model identification rate (TMIR) and the average model size. 

The authors thank an associate editor and two referees for their criticisms and constructive comments that lead to an improvement of the paper.