Perpendicular distance models for line transect sampling

Perpendicular distance line transect models are examined to assess whether any single model can provide a general procedure for analysing line transect data. Of the two-parameter models considered, the hazard-rate model appears promising, whereas the exponential power series and exponential quadratic models do not. Of the nonparametric models, the Fourier series is the best developed, and is favoured by many researchers as a general model. However, for a given data set, the Fourier series estimate may be highly dependent on the number of terms selected, and so the model is not a clear improvement over the hazard-rate model. A similar variable-term model, using Hermite polynomials, is considered, and is shown to be less dependent on the number of terms selected. There has been some debate about whether the derivative of the density function of perpendicular distances evaluated at 0 should be 0, so that the function has a "shoulder." The problem is examined in detail, and it is argued that reliable estimation is not possible from line transect data unless a shoulder exists. Many data sets appear to exhibit no shoulder; possible reasons are examined.