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Least median of squares: a suitable objective function for stock assessment models?
Shertzer, K.W.; Prager, M.H. (2002). Least median of squares: a suitable objective function for stock assessment models? Can. J. Fish. Aquat. Sci. 59(9): 1474-1481
In: Canadian Journal of Fisheries and Aquatic Sciences = Journal canadien des sciences halieutiques et aquatiques. National Research Council Canada: Ottawa. ISSN 0706-652X, more
Peer reviewed article  

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Keywords
    Fishery data; Models; Stock assessment; Marine

Authors  Top 
  • Shertzer, K.W.
  • Prager, M.H.

Abstract
    Robust fitting methods, intended for data sets possibly contaminated with invalid observations, are gaining increased use in analysis of fishery data. In particular, the method of least median of squares (LMS) has attracted attention. Its hallmark is high statistical resistance, which makes it immune to up to 50% contamination in the data. However, the same property makes it inefficient and can cause faulty fitting of typical fishery data. The LMS fit can be in conflict with important sections of a time series, a problem we illustrate by fitting a biomass dynamic (surplus production) model to simulated and actual fishery data. Additionally, we illustrate that LMS parameter estimates can be highly sensitive to small perturbations in the data. Other robust methods, like the method of least absolute values (LAV), appear less prone to such problems. A key reference on LMS recommends using the method as part of an exploratory procedure to identify outliers, rather than as an objective function for final model fitting. We concur with that recommendation.

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