## The Annals of Statistics

### On the Uniformity of Sequential Procedures

Raymond J. Carroll

#### Abstract

An extension of a central limit theorem for a mean of a random number of observations is given. A natural application occurs in the area of fixed-width confidence intervals. We provide an example which shows that the standard procedure does not preserve the intended coverage probability uniformly over nontrivial sets of distribution functions. The major weak convergence result is used to provide conditions for and a simple proof of such uniformity. The results are also shown to hold for $M$-estimates of location.

#### Article information

Source
Ann. Statist., Volume 5, Number 5 (1977), 1039-1046.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176343958

Digital Object Identifier
doi:10.1214/aos/1176343958

Mathematical Reviews number (MathSciNet)
MR451573

Zentralblatt MATH identifier
0368.62069

JSTOR