## The Annals of Statistics

- Ann. Statist.
- Volume 12, Number 2 (1984), 533-550.

### Sequential Determination of Estimator as Well as Sample Size

#### Abstract

For certain point and interval estimation problems, sequential procedures are proposed for choosing an estimator (from the class of trimmed means with trimming proportion in a specified range) as well as a sample size on which to base the estimator. It is shown that these procedures, which do not require knowledge of the best trimming proportion or the asymptotic variance of the corresponding trimmed mean, are asymptotically efficient with respect to the procedure that uses the best trimmed mean (in the specified class) and the best fixed sample size for that trimmed mean.

#### Article information

**Source**

Ann. Statist., Volume 12, Number 2 (1984), 533-550.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176346504

**Digital Object Identifier**

doi:10.1214/aos/1176346504

**Mathematical Reviews number (MathSciNet)**

MR740910

**Zentralblatt MATH identifier**

0544.62075

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62L12: Sequential estimation

Secondary: 62F35: Robustness and adaptive procedures 62G05: Estimation

**Keywords**

Sequential point estimation fixed-width confidence interval trimmed mean asymptotic efficiency adaptive estimation uniform integrability

#### Citation

Martinsek, Adam T. Sequential Determination of Estimator as Well as Sample Size. Ann. Statist. 12 (1984), no. 2, 533--550. doi:10.1214/aos/1176346504. https://projecteuclid.org/euclid.aos/1176346504