Abstract: We develop a new estimator of population size when data come from an independent double sampling experiment and at least one continuous covariate for each detection is measured. The new estimator has two features: (i) detection probabilities are estimated by non-parametric smoothing of redetections; (ii) population size is estimated with a Horvitz-Thompson type estimator. Expressions for asymptotic bias and variance are developed. The estimators are shown to be efficient when sampling is unbiased. We provide an illustration on two-stage recapture data on aboriginals in Canada.
Key words and phrases: Biased sampling, kernel regression, local linear estimator, Nadaraya-Watson estimator, wildlife abundance estimation.