• Auxiliary information;
  • Empirical likelihood method;
  • Loglinear model;
  • Model-assisted approach;
  • Nonparametric smoothing;
  • Survey design;
  • Variance estimation

Summary.  The fish abundance index over an ocean region is defined here to be the integral of expected catch per unit effort (CPUE), approximated by the sum of expected CPUE over grid squares. When trawl surveys are done within grid squares selected according to a probability sampling design, several other sources of variation such as the fish population dynamics and the catching process are also involved. In such situations model-assisted methods for estimating abundance, assessed under both design and model perspectives, have some advantages over purely design-based methods such as the Horvitz–Thompson (HT) estimator or purely model-based prediction approaches. This article develops model-assisted empirical likelihood (EL) methods via loglinear regression and nonparametric smoothing. The methods are applied to grid surveys of the Grand Bank region carried out annually by Fishery Products International from 1996 through 2002. The HT and EL methods produce similar point estimates of abundance indices. Simulation results, however, indicate that the EL estimator under local linear smoothing is associated with smaller standard errors.