A Weighted Duration-in-Beam Estimator for the Volume Sampled by a Quantitative Echo Sounder

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Abstract
Estimation of absolute fish density or abundance using the echo-count technique requires estimation of the volume sampled. The unknown parameter in the volume sampled is the sine of the half-angle of the effective conical beam. We derive the minimum variance, unbiased, linear estimator of this parameter. This estimator is based upon weighted regression through the origin and reduces to a computationally simple form. We use this estimate and its variance to estimate absolute density, absolute abundance, and their variances. We use a bootstrap procedure to contrast the performance of our method against that of a contemporary method, which is based upon the averages taken over range strata. Although both of these methods are unbiased, we show that our estimator has a standard deviation that is 23.5% smaller than that of the average-over-strata method.

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