###
SEQUENTIAL FIXED-WIDTH CONFIDENCE INTERVAL

FOR THE PRODUCT OF TWO MEANS

###
SHEN ZHENG, T. N. SRIRAM AND ANDREW F. SEILA

*Department of Statistics, Franklin College of Arts and Sciences, University of Georgia,*

204 Statistics Building, Athens, GA 30602, U.S.A.
(Received October 17, 1996; revised March 5, 1997)

**Abstract.**
For the product of two population
means, the problem of constructing a fixed-width
confidence interval with preassigned coverage
probability is considered. It is shown that the optimal
sample sizes which minimize the total sample size and
at the same time guarantee a fixed-width confidence
interval of desired coverage depend on the unknown
parameters. In order to overcome this, a fully
sequential procedure consisting of a sampling scheme
and a stopping rule are proposed. It is then shown that
the sequential confidence interval is asymptotically
consistent and the stopping rule is asymptotically
efficient, as the width goes to zero. Furthermore, a
second order result for the difference between the
expected stopping time and the (total) optimal fixed
sample size is established. The theoretical results are
supported by appropriate simulations.

*Key words and phrases*:
Coverage
probability, fully sequential procedure, sampling
scheme, asymptotic consistency, asymptotic efficiency,
uniform integrability.

**Source**
( TeX ,
DVI ,
PS )