## The Annals of Statistics

- Ann. Statist.
- Volume 11, Number 1 (1983), 296-305.

### Choosing Between Experiments: Applications to Finite Population Sampling

#### Abstract

Suppose that a statistician is faced with a decision problem involving an unknown parameter. Before making his decision he can carry out one of two possible experiments. Assume that he may choose at random which of the two experiments he will observe. For this problem a decision procedure for the statistician is a triple consisting of the randomizing probability measure he uses to choose between the experiments, the decision function he uses if he observes the first experiment and the decision function he uses if he observes the second experiment. The main theorem of this paper identifies the set of such admissible triples when the parameter space, and the sample spaces of the two experiments are finite. This result is then used to find some uniformly admissible procedures for some problems in finite population sampling.

#### Article information

**Source**

Ann. Statist., Volume 11, Number 1 (1983), 296-305.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176346080

**Digital Object Identifier**

doi:10.1214/aos/1176346080

**Mathematical Reviews number (MathSciNet)**

MR684887

**Zentralblatt MATH identifier**

0508.62012

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62C15: Admissibility

Secondary: 62D05: Sampling theory, sample surveys 62C10: Bayesian problems; characterization of Bayes procedures

**Keywords**

Choosing between experiments admissibility Bayes orthogonal priors finite population sampling uniform admissibility ratio estimator Horvitz-Thompson estimator Basu estimator choice of designs

#### Citation

Meeden, Glen; Ghosh, Malay. Choosing Between Experiments: Applications to Finite Population Sampling. Ann. Statist. 11 (1983), no. 1, 296--305. doi:10.1214/aos/1176346080. https://projecteuclid.org/euclid.aos/1176346080