Determination of the Maximum Foregut Volume of Western Rock Lobsters (Panulirus cygnus) from Field Data

• Published in: Biometrics Vol. 39; no. 3; pp. 543 - 551
• Main Authors: Maller, R. A., de Boer, E. S., Joll, L. M., Anderson, D. A., Hinde, J. P.
• Format: Journal Article
• Language: English
• Published: Biometric Society 01-09-1983
• Subjects: Biometrics; Data lines; Estimation bias; Estimation methods; Foregut; Least squares; Lobsters; Maximum likelihood estimation; Standard error; Statistical variance
• ISSN: 0006-341X; 1541-0420
• DOI: 10.2307/2531082

Two methods are presented for estimating the parameters of a line that describes the upper boundary of a triangular set of points. One method is a nonparametric maximum likelihood approach in which an unknown mixing distribution is introduced to account for the vertical spread of the points. The EM algorithm is used to maximize the likelihood. The other method is an iterative modification of the least squares procedure, in which points are weighted according to their distance from a trial line, and thus a new line is obtained; this forms the basis for the next iteration. This procedure is shown to be a one-sided trimming method, equivalent to the least squares line through a subset of the data. Estimates of the slope, intercept and residual variance are obtained from this subset in the usual way. The study was motivated by data on the foregut contents of the rock lobster Panulirus cygnus. The two methods give similar results when applied to these data. The first method requires a large number of iterations and is expensive; the second method is fast and inexpensive. Simulations of the estimates obtained by the second method show that biases are present, although small, and that the estimates of slope and intercept are approximately normally distributed.