Comment: Fisher Lecture: Dimension Reduction in Regression

Comment: Fisher Lecture: Dimension Reduction in Regression [arXiv:0708.3774]Comment: Published at http://dx.doi.org/10.1214/088342307000000050 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Split-plot designs: What, why, and how

The past decade has seen rapid advances in the development of new methods for the design and analysis of split-plot experiments. Unfortunately, the value of these designs for industrial experimentation has not been fully appreciated. In this paper, we review recent developments and provide guidelines for the use of split-plot designs in industrial applications

Multivariate Design of Experiments for Engineering Dimensional Analysis

We consider the design of dimensional analysis experiments when there is more than a single response. We first give a brief overview of dimensional analysis experiments and the dimensional analysis (DA) procedure. The validity of the DA method for univariate responses was established by the Buckingham $\Pi$-Theorem in the early 20th century. We extend the theorem to the multivariate case, develop basic criteria for multivariate design of DA and give guidelines for design construction. Finally, we illustrate the construction of designs for DA experiments for an example involving the design of a heat exchanger

Statistical Methods for Optimally Locating Automatic Traffic Recorders

This report presents new computer-based statistical methods for the optimal placement of automatic traffic recorders (ATR). The goal of each method is to locate a set of ATRs so as to improve the overall efficiency and accuracy of Annual Average Daily Traffic (AADT) estimates. The precise estimation of AADTs is essential because of the important role they play in many highway design, maintenance, and safety decisions. Because of the huge number of potential ATR sites in a typical state highway, optimal selection of ATR sites is a very large combinatorial problem. Accordingly, site selection is currently accomplished through judgmental and/or design-based sampling techniques (e.g., random sampling). By developing fast and efficient computer algorithms to accomplish the purposive selection of an optimal sample, we demonstrate that model-based sampling is a viable alternative to classical design-based sampling techniques. The algorithms developed in this project include an exchange algorithm and a two-stage sampling algorithm. In the rank-1 exchange algorithm, ATR sites are sequentially added to and deleted from the design. It generates highly efficient designs without exhaustively searching through all possible designs. In the two-stage sampling approach, similar sites are statistically clustered, then approximate design techniques are used to calculate the optimal weight for each cluster. Based on these optimal weights, a random sample of sites is selected from within each cluster. The speed of this two-stage sampling algorithm makes it an ideal approach for large-scale problems. Using traffic data provided by the Minnesota Department of Transportation, we demonstrate empirically that both algorithms are substantially better in terms of average variance of prediction than simple random sampling.University of Minnesota Center for Transportation Studies, U.S. Department of Transportation, and the Mountain-Plains Consortiu

A class of three-level designs for definitive screening in the presence of second-order effects

Screening designs are attractive for assessing the relative impact of a large number of factors on a response of interest. Experimenters often prefer quantitative factors with three levels over two-level factors because having three levels allows for some assessment of curvature in the factor–response relationship. Yet, the most familiar screening designs limit each factor to only two levels. We propose a new class of designs that have three levels, provide estimates of main effects that are unbiased by any second-order effect, require only one more than twice as many runs as there are factors, and avoid confounding of any pair of second-order effects. Moreover, for designs having six factors or more, our designs allow for the efficient estimation of the full quadratic model in any three factors. In this respect, our designs may render follow-up experiments unnecessary in many situations, thereby increasing the efficiency of the entire experimentation process. We also provide an algorithm for design construction

Effective Design-Based Model Selection for Definitive Screening Designs

<p>Since their introduction by Jones and Nachtsheim in <a href="#cit0010" target="_blank">2011</a>, definitive screening designs (DSDs) have seen application in fields as diverse as bio-manufacturing, green energy production, and laser etching. One barrier to their routine adoption for screening is due to the difficulties practitioners experience in model selection when both main effects and second-order effects are active. Jones and Nachtsheim showed that for six or more factors, DSDs project to designs in any three factors that can fit a full quadratic model. In addition, they showed that DSDs have high power for detecting all the main effects as well as one two-factor interaction or one quadratic effect as long as the true effects are much larger than the error standard deviation. However, simulation studies of model selection strategies applied to DSDs can disappoint by failing to identify the correct set of active second-order effects when there are more than a few such effects. Standard model selection strategies such as stepwise regression, all-subsets regression, and the Dantzig selector are general tools that do not make use of any structural information about the design. It seems reasonable that a modeling approach that makes use of the known structure of a designed experiment could perform better than more general purpose strategies. This article shows how to take advantage of the special structure of the DSD to obtain the most clear-cut analytical results possible.</p

Institute of Statistics Mimeo Series No. 2607 SIR 3: Dimension Reduction in the Presence of Linearly or Nonlinearly Related Predictors

Sufficient dimension reduction (sdr) is an effective tool for reducing highdimensional predictor spaces in regression problems. sdr achieves dimension reduction without loss of any regression information and without the need to assume any particular parametric form of a model. This is particularly useful for high-dimensional applications such as data mining, marketing, and bioinformatics. However, most sdr methods require a linearity condition on the predictor distribution, and that restricts the applications of sdr. In this article, we propose a new sdr method, sir3, which does not require the linearity condition, and which we show to be effective when nonlinearly-related predictors are present. sir3 is an extension of a representative sdr method sliced inverse regression (sir), and it is shown that sir3 reduces to sir when the linearity condition holds. A simulation study and a real data application are presented to demonstrate the effectiveness of the proposed method