## The Annals of Statistics

- Ann. Statist.
- Volume 7, Number 3 (1979), 644-652.

### Linear Estimation of the Probability of Discovering a New Species

#### Abstract

A population consisting of an unknown number of distinct species is searched by selecting one member at a time. No a priori information is available concerning the probability that an object selected from this population will represent a particular species. Based on the information available after an $n$-stage search it is desired to predict the conditional probability that the next selection will represent a species not represented in the $n$-stage sample. Properties of a class of predictors obtained by extending the search an additional $m$ stages beyond the initial search are exhibited. These predictors have expectation equal to the unconditional probability of discovering a new species at stage $n + 1$, but may be strongly negatively correlated with the conditional probability.

#### Article information

**Source**

Ann. Statist. Volume 7, Number 3 (1979), 644-652.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

http://projecteuclid.org/euclid.aos/1176344684

**Digital Object Identifier**

doi:10.1214/aos/1176344684

**Mathematical Reviews number (MathSciNet)**

MR527498

**Zentralblatt MATH identifier**

0405.62025

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62F10: Point estimation

**Keywords**

2A99 Linear unbiased estimation prediction search probabilities species Vandermonde determinant

#### Citation

Starr, Norman. Linear Estimation of the Probability of Discovering a New Species. Ann. Statist. 7 (1979), no. 3, 644--652. doi:10.1214/aos/1176344684. http://projecteuclid.org/euclid.aos/1176344684.