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Activity Number: 78 - Nonparametric Modeling
Type: Contributed
Date/Time: Sunday, July 28, 2019 : 4:00 PM to 5:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract #306452
Title: Targeted Learning of the Population Size Based on Capture-Recapture Designs
Author(s): Yue You* and Mark van der Laan and Nicholas Jewell and Robin Mejia
Companies: Biostatistics, UC Berkeley and UC Berkeley and Biostatistics, UC Berkeley and Carnegie Mellon University
Keywords: Asymptotic linear estimator; capture-recapture; MLE; influence curve; targeted maximum likelihood estimation (TMLE); population size

We propose a method to estimate population size based on capture-recapture designs of K samples. The observed data is formulated as a biased sample of n iid K-dimensional vectors of binary indicators from a conditional distribution given the vector is not 0, where the k-th component indicates that subject being caught by the k-th sample. The target quantity is the prob. that the vector is not 0. We cover models assuming a single general constraint on the K-dimensional distribution so that the target quantity is identified and the statistical model is unrestricted. We present worked out solutions for common constraints (K-way additive interaction=0 and conditional independence). We show the dramatic impact of the choice of constraint on the estimand value, so it’s crucial for the constraint to hold by design. For the K-way multiplicative interaction=0 constraint, MLE suffers from the curse of dimensionality. We propose a targeted MLE that combines machine learning to smooth across the 2^K cells while targeting the fit towards the target parameter of interest. For each problem, we provide simulations wrt assumption violations, inference with CI and experimental designs with software.

Authors who are presenting talks have a * after their name.

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