### Abstract

Duration-in-beam is the most reliable procedure for estimating acoustical sample volume when the target strength is unknown. In this paper, duration-in-beam data are examined using four different statistical procedures for calibration, the method of moments estimator (MME), the best linear unbiased estimator (BLUE), the median-based estimator (MBE), and the maximum likelihood estimator (MLE). The MME generally has a small bias. The BLUE is approximately unbiased and reduces the standard error by 16% from the MME for a representative data set. The MBE is medianunbiased but biased and increases the standard error by 35% relative to the BLUE for the data set examined. However, the MBE is less sensitive to outliers than the BLUE. The MME, BLUE, and MBE are consistent: that is, they converge to the true value with zero variance as the sample size goes to infinity. In contrast, the MLE is not consistent, is biased, and its value is determined by the most extreme outlier, making this estimator's properties unacceptable. The conclusion drawn is that the success or failure of acoustically estimating fish populations can be dependent upon the methods of statistical analysis where precision of the estimate is important.

Original language | English |
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Pages (from-to) | 197-208 |

Number of pages | 12 |

Journal | Fisheries Research |

Volume | 14 |

Issue number | 2-3 |

DOIs | |

State | Published - Jan 1 1992 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Aquatic Science

### Cite this

**A comparison of four duration-in-beam estimators for the sine of the half-angle of the effective conical volume sampled.** / Crittenden, Robert N.; Thomas, Gary.

Research output: Contribution to journal › Article

*Fisheries Research*, vol. 14, no. 2-3, pp. 197-208. https://doi.org/10.1016/0165-7836(92)90053-V

}

TY - JOUR

T1 - A comparison of four duration-in-beam estimators for the sine of the half-angle of the effective conical volume sampled

AU - Crittenden, Robert N.

AU - Thomas, Gary

PY - 1992/1/1

Y1 - 1992/1/1

N2 - Duration-in-beam is the most reliable procedure for estimating acoustical sample volume when the target strength is unknown. In this paper, duration-in-beam data are examined using four different statistical procedures for calibration, the method of moments estimator (MME), the best linear unbiased estimator (BLUE), the median-based estimator (MBE), and the maximum likelihood estimator (MLE). The MME generally has a small bias. The BLUE is approximately unbiased and reduces the standard error by 16% from the MME for a representative data set. The MBE is medianunbiased but biased and increases the standard error by 35% relative to the BLUE for the data set examined. However, the MBE is less sensitive to outliers than the BLUE. The MME, BLUE, and MBE are consistent: that is, they converge to the true value with zero variance as the sample size goes to infinity. In contrast, the MLE is not consistent, is biased, and its value is determined by the most extreme outlier, making this estimator's properties unacceptable. The conclusion drawn is that the success or failure of acoustically estimating fish populations can be dependent upon the methods of statistical analysis where precision of the estimate is important.

AB - Duration-in-beam is the most reliable procedure for estimating acoustical sample volume when the target strength is unknown. In this paper, duration-in-beam data are examined using four different statistical procedures for calibration, the method of moments estimator (MME), the best linear unbiased estimator (BLUE), the median-based estimator (MBE), and the maximum likelihood estimator (MLE). The MME generally has a small bias. The BLUE is approximately unbiased and reduces the standard error by 16% from the MME for a representative data set. The MBE is medianunbiased but biased and increases the standard error by 35% relative to the BLUE for the data set examined. However, the MBE is less sensitive to outliers than the BLUE. The MME, BLUE, and MBE are consistent: that is, they converge to the true value with zero variance as the sample size goes to infinity. In contrast, the MLE is not consistent, is biased, and its value is determined by the most extreme outlier, making this estimator's properties unacceptable. The conclusion drawn is that the success or failure of acoustically estimating fish populations can be dependent upon the methods of statistical analysis where precision of the estimate is important.

UR - http://www.scopus.com/inward/record.url?scp=0027038899&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027038899&partnerID=8YFLogxK

U2 - 10.1016/0165-7836(92)90053-V

DO - 10.1016/0165-7836(92)90053-V

M3 - Article

VL - 14

SP - 197

EP - 208

JO - Fisheries Research

JF - Fisheries Research

SN - 0165-7836

IS - 2-3

ER -