Abstract: We study capture-recapture models in a closed population when multiple error-prone measurements of a covariate are available. Due to the identity between the number of captures and the number of measurements, no suitable complete and sufficient statistic exists, and the existing method no longer applies. The familiar strategy of generalized method of moments fails to resolve this issue satisfactorily, and complexity lies in the loss of the surrogacy assumption commonly assumed in measurement error problems. Our approach to this problem through a semiparametric treatment overcomes these difficulties. The superior performance of the new method is demonstrated through numerical experiments in simulated and data examples.

Key words and phrases: Capture-recapture, complete sufficient statistic, generalized method of moments, measurement error, semiparametrics, surrogacy.