Steven F. Arnold

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 these samples are used to draw conclusions about the true distribution function using very few assumptions.

Representative publications

Arnold, S. F. 1981. The Theory of Linear Models and Multivariate Analysis. New York, NY: Wiley.

Byrne, P. J., and S. F. Arnold. 1983. Repeated measures analysis for a time series model. Journal of the American Statistical Association 78:850-855.

Arnold, S. F. 1984. The asymptotic validity of invariant procedures for the repeated measures model and multivariate linear model. Journal of Multivariate Analysis 15:325-335.

Arnold, S. F. 1984. Pivotal quantities and invariant confidence regions. Statistics and Decisions 2:257-280.

Arnold, S. F. 1990. Mathematical Statistics. Englewood Cliffs, NJ: Prentice Hall.