SCHEDULE

ABSTRACTS

Measuring objects and holes, I
Nell Sedransk
National Institute of Statistical Sciences

Objects and holes exist in 3-space. Unstable axes or centroids distort 3-dimensional shapes, while dents, bulges, creases, ridges, pits and nubs perturb smooth shapes locally, regionally and/or globally. Making inference depends on the measurement process; designing an efficient measurement process is a 3-dimensional challenge and often simultaneously a 2-dimensional and 1-dimensional challenge as well. The problem of experimental design is examined for two very different (engineering) contexts and from two different vantage points; the first is centered inside, and the second is centered outside.
 
Design and Analysis when the Center is Internal
 
The range of controllable arm motion for a patient with a spinal cord injury exists as an imaginary object, often with a vacuous center. Expansion of this "controllable space" is a metric for assessing success of a therapeutic intervention or progressing degradation of function through stricture or muscle weakness and failure. Inference about changes in the controllable space depends upon the measurement protocol, i.e., the experimental design. Patient fatigue during the measurement process severely limits the number of trials. Bayesian methods for inference as well as design offer some solutions for making inferences about the shape of the controllable space and that of its vacuous center.

Measuring objects and holes, II
Nell Sedransk
National Institute of Statistical Sciences

Objects and holes exist in 3-space. Unstable axes or centroids distort 3-dimensional shapes, while dents, bulges, creases, ridges, pits and nubs perturb smooth shapes locally, regionally and/or globally. Making inference depends on the measurement process; designing an efficient measurement process is a 3-dimensional challenge and often simultaneously a 2-dimensional and 1-dimensional challenge as well. These examples illustrate the transfer classical experimental design principles to modern, non-standard experimental situations.
 
Design and Analysis when the Vantage Point is External
 
High-precision is required for reflective and optical surfaces that are used from the megamacro- to the nano-scale in state-of-the-art scientific equipment from telescopes to scanning tunneling electron microscopes. Standard objects for calibration of such equipment must be ultra-smooth and as perfectly formed as is possible with current technology. The canonical, but real, problem is the manufacturing of a perfect sphere. Local curvature can be measured, pointwise from the surface, by refraction. The design strategy is to proceed from the global form down to the surface details.

On a simple measure of dominance
Calvin Berry
University of Louisiana at Lafayette

One way to describe how much better treatment Y is than treatment X is to find a response value such that the probability of Y being better than this value is the same as the probability of X being worse. We consider the size of this probability as a measure dom(F_Y,F_X) of the dominance of Y over X. Thus we label the central point at which the graph of F_X(x) meets the graph of 1-F_Y(x) as (xdom(F_Y,F_X), dom(F_Y,F_X)). Conditions are given for the asymptotic normality of (xdom(Ghat,Fhat), dom(Ghat,Fhat)) when Ghat and Fhat are possibly dependent empirical distributions. A Wilson--type approximate confidence interval for dom(G,F) is proposed and this interval is shown to perform generally better than a Wald--type interval.

Biased bootstrap methods for GMM models
Mihai C Giurcanu
University of Louisiana at Lafayette

I will discuss a new biased--bootstrap method for generalized method of moments (GMM) models. Calibration of this procedure will be facilitated by the development of a biased--bootstrap recycling algorithm to control the cost of bootstrap iteration. The resulting methodology is a competitor of the jackknife--after--bootstrap developed by Efron(1992). The biased--bootstrap is a form of weighted bootstrap with weights chosen to satisfy the constraints imposed by the statistical model. First, a pseudo--parametric family of weighted empirical distributions is constructed, obtained by minimizing the Cressie--Read distance to the empirical distribution under the constraints imposed by the model. By resampling within this family, the biased--bootstrap "mimics" the parametric bootstrap for semiparametric models. Because of its non--parametric nature, the biased--bootstrap can be iterated using importance sampling to reweight the first level bootstrap resamples, resulting in an efficient bootstrap recycling algorithm. An application to the bootstrap calibrated confidence intervals will be provided.

ROC analysis of dropout indicators
James J. Madden
Louisiana State University

The parameter A, which denotes the area under the receiver operating characteristic (ROC) curve, is a useful measure of the quality of a diagnostic test; see John A. Swets, Measuring the Accuracy of Diagnostic Systems, Science, New Series, Vol. 240, No. 4857. (Jun. 3, 1988), pp. 1285-1293. We determined the value A for several different early indicators used to predict dropping out of school. The best among them is the grade-point average in core subjects. As a diagnostic test, this works about as well as mammography does for breast-cancer detection.

The Skew-Normal Distribution and Its Application
Nabendu Pal
University of Louisiana at Lafayette

The Skew-Normal distribution (SND), which is a generalization of the usual normal distribution, incorporates skewed shape of the pdf, and hence it is more versatile in fitting real-life datasets. Though the SND has some nice properties, it has its own share of difficulties which prevents one from making the full use of the distribution. In this talk we'll discuss the challenges one faces with the SND. We'll also present a generalization of the Stein's normal identity which enables one to derive suitable expectations of the SND easily.