93JCGS02\P0131-------------------------------------------------------
A Stochastic Shape and Color Model for Defect Detection in Potatoes
Ulf Grenander and Kevin M. Manbeck
Automatic defect detection in color images of potatoes is
complicated by the random variability ordinarily observed in a
collection of normal potatoes. Stochastic models are developed that
explicitly describe the random nature of the shape and color texture
observed in normal potatoes. Shape and color simulations based on
these models are realistic. Statistical tests based on the stochastic
shape and color models are developed. The tests are capable of
classifying an unknown object as either ``acceptable potato'' or
``unacceptable potato.'' Twelve potatoes are analyzed, and the
experimental results are presented.
Key Words: Deformable template; Image analysis; Maximum likelihood;
Stochastic difference equation; von Mises distribution.
93JCGS02\P0153-------------------------------------------------------
Dotplot: A Program for Exploring Self-Similarity in Millions of
Lines of Text and Code
Kenneth Ward Church and Jonathan Isaac Helfman
An interactive program, dotplot, has been developed for browsing
millions of lines of text and source code, using an approach borrowed
from biology for studying homology (self-similarity) in DNA sequences.
With conventional browsing tools such as a screen editor, it is
difficult to identify structures that are too big to fit on the
screen. In contrast, with dotplots we find that many of these
structures show up as diagonals, squares, textures and other visually
recognizable features, as will be illustrated in examples selected
from biology and two new application domains, text (AP news, Canadian
Hansards) and source code (5ESS). In an attempt to isolate the
mechanisms that produce these features, we have synthesized similar
features in dotplots of artificial sequences. We also introduce an
approximation that makes the calculation of dotplots practical for use
in an interactive browser.
Key Words: Biology; Corpora; Duplication; Scatterplot; Software engineering;
String matching.
93JCGS02\P0175-------------------------------------------------------
Normal/Independent Distributions and Their Applications
in Robust Regression
Kenneth Lange and Janet S. Sinsheimer
Maximum likelihood estimation with nonnormal error distributions
provides one method of robust regression. Certain families of
normal/independent distributions are particularly attractive for
adaptive, robust regression. This article reviews the properties of
normal/independent distributions and presents several new results.
A major virtue of these distributions is that they lend themselves to
EM algorithms for maximum likelihood estimation. EM algorithms are
discussed for least $L_p$ regression and for adaptive, robust
regression based on the $t$, slash, and contaminated normal
families. Four concrete examples illustrate the performance of the
different methods on real data.
Key Words: EM algorithm; Normal/independent distribution; Robust regression.
93JCGS02\P0199-------------------------------------------------------
A Method for the Computer Calculation of Edgeworth Expansions
for Smooth Function Models
Paul Kabaila
In this article I describe, in detail, a method for the computer
calculation of Edgeworth expansions for a smooth function
model accurate in the $O(n^{-1})$ term. For such models, these
expansions are an important tool for the analysis of normalizing
transformations, the correction of an approximately normally distributed
quantity for skewness, and the comparison of bootstrap
inference procedures. The method is straightforward and is
efficient in a sense described in the article. The implementation
of the method in general is clear from its implementation in the
Mathematica program (available through StatLib) for the particular
case of the studentized mean.
Key Words: Asymptotic expansions for moments; Bootstrap; Edgeworth
expansion; Mathematica; Symbolic computation.
93JCGS02\P0209-------------------------------------------------------
Characterizing and Generating Bivariate Empirical Rank Distributions
Satisfying Certain Positive Dependence Concepts
Magdy H. Metry and Allan R. Sampson
This article introduces an approach for characterizing the
classes of empirical distributions that satisfy certain positive
dependence notions. Mathematically, this can be expressed as studying
certain subsets of the class $S_N$ of permutations of $1, \ldots, N$,
where each subset corresponds to some positive dependence notions.
Explicit techniques for iteratively characterizing subsets of $S_N$
that satisfy certain positive dependence concepts are obtained and
various counting formulas are given. Based on these techniques,
graph theoretic methods are used to introduce new and more efficient
algorithms for constructively generating and enumerating the elements
of various of these subsets of $S_N$. For example, the class of
positively quadrant dependent permutations in $S_N$ is characterized
in this fashion.
Key Words: Counting; Empirical (rank) distribution function; Graph
algorithms; More concordant partial ordering; Permutation; Positive
dependence properties.