Doubly robust capture-recapture methods for estimating population size

Abstract

Estimation of population size using incomplete lists (also called the capture-recapture problem) has a long history across many biological and social sciences. For example, human rights and other groups often construct partial and overlapping lists of victims of armed conflicts, with the hope of using this information to estimate the total number of victims. Earlier statistical methods for this setup either use potentially restrictive parametric assumptions, or else rely on typically suboptimal plug-in-type nonparametric estimators; however, both approaches can lead to substantial bias, the former via model misspecification and the latter via smoothing. Under an identifying assumption that two lists are conditionally independent given measured covariate information, we make several contributions. First we derive the nonparametric efficiency bound for estimating the capture probability, which indicates the best possible performance of any estimator, and sheds light on the statistical limits of capture-recapture methods. Then we present a new estimator, and study its finite-sample properties, showing that it has a double robustness property new to capture-recapture, and that it is near-optimal in a non-asymptotic sense, under relatively mild nonparametric conditions. Next, we give a method for constructing confidence intervals for total population size from generic capture probability estimators, and prove non-asymptotic nearvalidity. Finally, we study our methods in simulations, and apply them to estimate the number of killings and disappearances attributable to different groups in Peru during its internal armed conflict between 1980 and 2000.

drpop: Efficient and Doubly Robust Population Size Estimation in R

“…The main goal of drpop is to improve estimation while using complex covariate information to model the heterogeneity. Unlike existing software, the methods in drpop are fully nonparametric, doubly robust, and optimally efficient under weak nonparametric conditions [Das et al, 2021]. drpop also lets the user apply their choice of flexible model(s) to capture the heterogeneity in the data.…”

“…Starting in section 2, we discuss the data structure for capture-recapture problems and introduce the necessary notations and the identification assumption. In section 3, we briefly present the estimation method from Das et al [2021] to obtain a doubly robust efficient estimator and the formula to obtain a confidence interval. Following this in section 4, we present some examples on how to use the drpop for different data types or problems and interpretation of the results.…”

“…Thus, to ensure identifiability of the total population size, we need some lack of dependence assumption among the lists. Das et al [2021] assumes that two lists out of the K lists are collected independently conditioned on the covariate(s). Without loss of generality one can assume that lists 1 and 2 are conditionally independent.…”

“…In the presence of covariates, one can use mild assumptions to ensure identifiability. Das et al [2021], Huggins [1989], Tilling and Sterne [1999] among others assumed that two lists are independent conditional on the covariate and presented non-parametric estimators. This conditional independence assumption is milder than the marginal independence assumption.…”

“…drpop implements the doubly robust estimators of capture probability and population size from Das et al [2021], which rely on assuming two lists are only conditionally rather than marginally independent. These methods are flexible yet efficient, with small mean squared error even in nonparametric models involving continuous or high-dimensional covariates.…”