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Biometrika 2000 87(3):633-649; doi:10.1093/biomet/87.3.633
© 2000 by Biometrika Trust
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A nonparametric approach to the analysis of two-stage mark-recapture experiments

SX Chen and CJ LloydZ

Department of Statistics and Applied Probability, National University of Singapore, Singapore 117 543 E-mail: songxichen@yahoo.com Z Australian Graduate School of Management, Sydney, NSW 2052, Australia E-mail: chrisl@agsm.unsw.edu.au

We present a new approach to the analysis of two-stage mark-recapture experiments where individual covariates are available which describe the detectability of individuals in the population. Central to the theory is a single quantity {alpha}, which we call the heterogeneity index and which measures the variability in the detectability of individuals. This theory also has implications for the analysis of independent observer line transect surveys. An estimator of {alpha} is provided by combining kernel density estimates of the underlying densities of the covariate, conditional on capture histories. We derive expressions for the asymptotic bias and variance and show that our new estimator is as efficient as the Petersen estimator when individuals all have the same detectability. We also report the results of a simulation study of the new estimator for a range of mark-recapture conditions.

Key Words: heterogeneity; kernel density estimation; weighted distribution


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