variance delta method

[PABLO PALENCIA MAYORDOMO]

Dear all,

I come with a statistical question related to variance estimation of density.

If I'm right, when applying distance sampling the variance of density is estimated using delta method and considering the variance of encounter rate, detection function...(Buckland 2001: pag. 76 eqn: 3.68), but assuming no correlation between these components, and in consequence, covariances are not considered (Buckland 2001: pag 52).

However, recently I read that if variables are correlated, covariances should be also considering when using delta method, and not only variances.

So, do current functions (R and Distance software) considered covariances when estimating density variance?

if not, why it is not considered? maybe because strong covariances are not expected? could it introduce bias (over or underestimation of precision)?

Thank you very much in advance :)

Pablo

[Eric Rexstad]

Pablo

You are correct about the delta method and its assumptions, that is why the delta method is considered an approximate method for computing precision.

If you are uncomfortable with the assumption of independence between components in distance sampling analysis, the preferred solution is to use a nonparametric bootstrap to measure uncertainty in your density estimates.   Both the Distance for Windows software as well as the Distance R package contain routines for constructing measures of precision using bootstraps; usually by resampling transects (points or lines) with replacement.

Consult Section 5.7.2 of Buckland et al. (2001) for a discussion of bootstrapping in the context of point transects.

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Eric Rexstad
Centre for Ecological and Environmental Modelling
University of St Andrews
St Andrews is a charity registered in Scotland SC013532

[PABLO PALENCIA MAYORDOMO]

Great, thank you very much Eric