Professor of Statistics
Ph.D., Stanford University, 1970
Summary of research interests
Dr. Arnold is studying the effect of reducing by
invariance before applying likelihood procedures. Examples
indicate that in many situations the likelihood procedures
are improved and in nearly all situations they are
no worse for this reduction. Certain types of invariance
reductions may lead to generalization of the idea of
ancillary statistics. Unfortunately, however, there
are situations in which reducing by invariance may
adversely affect likelihood procedures. Dr. Arnold
hopes to find out when the invariance reduction can
be taken safely and when it may lead to trouble.
His main research interest is statistical inference
for models involving patterned covariance matrices.
Although some attention is paid to methods for testing
for the adequacy of these models, the primary emphasis
is on finding procedures for drawing inference for
the mean vector when we assume that the covariance
matrix has the assumed structure. Recently, he has
been studying antedependence models.
A second research interest is in improved estimators
of the distribution function of samples of independently
identically distributed random variables. One goal
of this research is to find improved methods of doing
bootstrapping, a procedure in which repeated samples
are taken from the estimated distribution function
and used to draw conclusions about the true distribution
function using very few assumptions.
Representative publications
M. G. Akritas, S. F. Arnold, and Y. Du. 2000. Models
and methods for nonlinear analysis of covariance. Biometrika 87:
507-526.
M. G. Akritas and S. F. Arnold. 1994. Fully nonparametric
hypotheses for factorial designs I: Multivariate repeated
measures designs. JASA 89: 336-343.
S. F. Arnold. 1990. Mathematical Statistics.
Englewood Cliffs, NJ: Prentice Hall.
S. F. Arnold. 1984. The asymptotic validity of invariant
procedures for the repeated measures model and multivariate
linear model. Journal of Multivariate Analysis 15:325-335.
P. J. Byrne and S. F. Arnold. 1983. Repeated measures
analysis for a time series model. JASA 78:850-855.
Arnold, S. F. 1981. The Theory of Linear Models
and Multivariate Analysis. New York, NY: John
Wiley and Sons.
Last updated: April
10, 2003 |
