Doubly Robust Capture-Recapture Methods for Estimating Population Size

References

• Alho, J. M. (1990), “Logistic Regression in Capture-Recapture Models,” Biometrics, 46, 623–635.
   PubMed Web of Science ®Google Scholar
• Ball, P., Asher, J., Sulmont, D., and Manrique, D. (2003), How Many Peruvians have Died, Washington, DC: American Association for the Advancement of Science.
   Google Scholar
• Bickel, P. J., Klaassen, C. A., Bickel, P. J., Ritov, Y., Klaassen, J., Wellner, J. A., and Ritov, Y. (1993), Efficient and Adaptive Estimation for Semiparametric Models (Vol. 4), Baltimore: Johns Hopkins University Press.
   Google Scholar
• Bickel, P. J., and Ritov, Y. (1988), “Estimating Integrated Squared Density Derivatives: Sharp Best Order of Convergence Estimates,” Sankhyā: The Indian Journal of Statistics, Series A, 50, 381–393.
   Google Scholar
• Breslow, N. E., Robins, J. M., and Wellner, J. A. (2000), “On the Semi-Parametric Efficiency of Logistic Regression under Case-Control Sampling,” Bernoulli, 6, 447–455. DOI: 10.2307/3318670.
   Web of Science ®Google Scholar
• Burnham, K. P., and Overton, W. S. (1979), “Robust Estimation of Population Size When Capture Probabilities Vary Among Animals,” Ecology, 60, 927–936. DOI: 10.2307/1936861.
   Web of Science ®Google Scholar
• Carothers, A. (1973), “The Effects of Unequal Catchability on Jolly-Seber Estimates,” Biometrics, 29, 79–100. DOI: 10.2307/2529678.
   Web of Science ®Google Scholar
• Chao, A. (1987), “Estimating the Population Size for Capture-Recapture Data with Unequal Catchability,” Biometrics, 43, 783–791.
   PubMed Web of Science ®Google Scholar
• Chen, S. X., and Lloyd, C. J. (2000), “A Nonparametric Approach to the Analysis of Two-Stage Mark-Recapture Experiments,” Biometrika, 87, 633–649. DOI: 10.1093/biomet/87.3.633.
   Web of Science ®Google Scholar
• Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., and Newey, W. (2017), “Double/Debiased/Neyman Machine Learning of Treatment Effects,” American Economic Review, 107, 261–265. DOI: 10.1257/aer.p20171038.
   Web of Science ®Google Scholar
• Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W., and Robins, J. (2018), “Double/Debiased Machine Learning for Treatment and Structural Parameters,” The Econometrics Journal, 21, C1–C68. DOI: 10.1111/ectj.12097.
   Web of Science ®Google Scholar
• Darroch, J. N. (1958), “The Multiple-Recapture Census, I. Estimation of a Closed Population,” Biometrika, 45, 343–349. DOI: 10.2307/2333183.
   Web of Science ®Google Scholar
• Das, M., and Kennedy, E. H. (2021), “drpop: Efficient and Doubly Robust Population Size Estimation in R,” arXiv preprint arXiv:2111.07191.
   Google Scholar
• Evans, M. A., Kim, H.-M., and O’Brien, T. E. (1996), “An Application of Profile-Likelihood based Confidence Interval to Capture: Recapture Estimators,” Journal of Agricultural, Biological, and Environmental Statistics, 1, 131–140. DOI: 10.2307/1400565.
   Google Scholar
• Farrell, M. H. (2015), “Robust Inference on Average Treatment Effects with Possibly more Covariates than Observations,” Journal of Econometrics, 189, 1–23. DOI: 10.1016/j.jeconom.2015.06.017.
   Web of Science ®Google Scholar
• Fienberg, S. E. (1972), “The Multiple Recapture Census for Closed Populations and Incomplete 2k Contingency Tables,” Biometrika, 59, 591–603.
   Web of Science ®Google Scholar
• Fienberg, S. E., Johnson, M. S., and Junker, B. W. (1999), “Classical Multilevel and Bayesian Approaches to Population Size Estimation Using Multiple Lists,” Journal of the Royal Statistical Society, Series A, 162, 383–405. DOI: 10.1111/1467-985X.00143.
   Web of Science ®Google Scholar
• Friedrich, K. O. (1989), “A Berry-Esseen Bound for Functions of Independent Random Variables,” The Annals of Statistics, 17,170–183. DOI: 10.1214/aos/1176347009.
   Web of Science ®Google Scholar
• Gimenez, O., Choquet, R., Lamor, L., Scofield, P., Fletcher, D., Lebreton, J.-D., and Pradel, R. (2005), “Efficient Profile-Likelihood Confidence Intervals for Capture-Recapture Models,” Journal of Agricultural, Biological, and Environmental Statistics, 10, 184–196. DOI: 10.1198/108571105X46462.
   Web of Science ®Google Scholar
• Goudie, I. B., and Goudie, M. (2007), “Who Captures the Marks for the Petersen Estimator?” Journal of the Royal Statistical Society, Series A, 170, 825–839. DOI: 10.1111/j.1467-985X.2007.00479.x.
   Web of Science ®Google Scholar
• Györfi, L., Kohler, M., Krzyzak, A., and Walk, H. (2006), A Distribution-Free Theory of Nonparametric Regression, New York: Springer.
   Google Scholar
• Hald, A. (2003), A History of Probability and Statistics and their Applications before 1750 (Vol. 501), Hoboken, NJ: Wiley.
   Google Scholar
• Hernan, M. A., and Robins, J. M. (2019), Causal Inference, Boca Raton, FL: CRC.
   Google Scholar
• Huggins, R. (1989), “On the Statistical Analysis of Capture Experiments,” Biometrika, 76, 133–140. DOI: 10.1093/biomet/76.1.133.
   Web of Science ®Google Scholar
• Huggins, R., and Hwang, W.-H. (2007), “Non-Parametric Estimation of Population Size from Capture–Recapture Data when the Capture Probability depends on a Covariate,” Journal of the Royal Statistical Society, Series C, 56, 429–443. DOI: 10.1111/j.1467-9876.2007.00585.x.
   Web of Science ®Google Scholar
• Huggins, R., and Hwang, W.-H. (2011), “A Review of the Use of Conditional Likelihood in Capture-Recapture Experiments,” International Statistical Review, 79, 385–400.
   Web of Science ®Google Scholar
• Johndrow, J. E., Lum, K., and Manrique-Vallier, D. (2019), “Low-Risk Population Size Estimates in the Presence of Capture Heterogeneity,” Biometrika, 106, 197–210. DOI: 10.1093/biomet/asy065.
   Web of Science ®Google Scholar
• Kennedy, E. H. (2016), “Semiparametric Theory and Empirical Processes in Causal Inference,” in Statistical Causal Inferences and their Applications in Public Health Research, eds. H. He, P. Wu, D.-G. (Din) Chen, pp. 141–167, Cham: Springer.
   Google Scholar
• Kennedy, E. H. (2019), “Nonparametric Causal Effects based on Incremental Propensity Score Interventions,” Journal of the American Statistical Association, 114, 645–656.
   Web of Science ®Google Scholar
• Kurtz, Z. T. (2014), “Local Log-Linear Models for Capture-Recapture.” Doctoral dissertation, Carnegie Mellon University.
   Google Scholar
• Lee, S.-M., and Chao, A. (1994), “Estimating Population Size via Sample Coverage for Closed Capture-Recapture Models,” Biometrics, 50, 88–97.
   PubMed Web of Science ®Google Scholar
• Lincoln, F. C. (1930), Calculating Waterfowl Abundance on the Basis of Banding Returns, Number 118. US Department of Agriculture.
   Google Scholar
• Link, W. A. (2003), “Nonidentifiability of Population Size from Capture-Recapture Data with Heterogeneous Detection Probabilities,” Biometrics, 59, 1123–1130. DOI: 10.1111/j.0006-341x.2003.00129.x.
   PubMed Web of Science ®Google Scholar
• Manrique-Vallier, D. (2016), “Bayesian Population Size Estimation using Dirichlet Process Mixtures,” Biometrics, 72, 1246–1254. DOI: 10.1111/biom.12502.
   PubMed Web of Science ®Google Scholar
• Manrique-Vallier, D., and Ball, P. (2019), “Reality and Risk: A Refutation of S. Rendón’s Analysis of the Peruvian Truth and Reconciliation Commission’s Conflict Mortality Study,” Research & Politics, 6, 2053168019835628. DOI: 10.1177/2053168019835628.
   Web of Science ®Google Scholar
• Manrique-Vallier, D., Ball, P., and Sulmont, D. (2019), “Estimating the Number of Fatal Victims of the Peruvian Internal Armed Conflict, 1980-2000: An Application of Modern Multi-List Capture-Recapture Techniques,” arXiv preprint arXiv:1906.04763.
   Google Scholar
• Petersen, C. G. J. (1896), “The Yearly Immigration of Young Plaice in the Limfjord from the German Sea,” Report of the Danish Biological Station, 6, 1–48.
   Google Scholar
• Petersen, M. L., Porter, K. E., Gruber, S., Wang, Y., and Van Der Laan, M. J. (2012), “Diagnosing and Responding to Violations in the Positivity Assumption,” Statistical Methods in Medical Research, 21, 31–54. DOI: 10.1177/0962280210386207.
   PubMed Web of Science ®Google Scholar
• Pledger, S. (2000), “Unified Maximum Likelihood Estimates for Closed Capture–Recapture Models Using Mixtures,” Biometrics, 56, 434–442. DOI: 10.1111/j.0006-341x.2000.00434.x.
   PubMed Web of Science ®Google Scholar
• Pollock, K. H. (2002), “The Use of Auxiliary Variables in Capture-Recapture Modelling: An Overview,” Journal of Applied Statistics, 29, 85–102. DOI: 10.1080/02664760120108430.
   Web of Science ®Google Scholar
• Pollock, K. H., Nichols, J. D., Brownie, C., and Hines, J. E. (1990), “Statistical Inference for Capture-Recapture Experiments,” Wildlife Monographs, 107, 3–97.
   Google Scholar
• Qin, J. (2017), Biased Sampling, Over-identified Parameter Problems and Beyond, Singapore: Springer.
   Google Scholar
• Rendón, S. (2019), “Capturing Correctly: A Reanalysis of the Indirect Capture–Recapture Methods in the Peruvian Truth and Reconciliation Commission,” Research & Politics, 6, 2053168018820375.
   Web of Science ®Google Scholar
• Robins, J., Li, L., Tchetgen, E., and van der Vaart, A. (2008), “Higher Order Influence Functions and Minimax Estimation of Nonlinear Functionals,” in Probability and Statistics: Essays in Honor of David A. Freedman, eds. D. Nolan, and T. Speed, pp. 335–421, Beachwood, OH: Institute of Mathematical Statistics.
   Google Scholar
• Schnabel, Z. E. (1938), “The Estimation of the Total Fish Population of a Lake,” The American Mathematical Monthly, 45, 348–352. DOI: 10.2307/2304025.
   Google Scholar
• Sekar, C. C., Deming, W. E. (1949), “On a Method of Estimating Birth and Death Rates and the Extent of Registration,” Journal of the American Statistical Association, 44, 101–115. DOI: 10.1080/01621459.1949.10483294.
   Web of Science ®Google Scholar
• Stoklosa, J., and Huggins, R. M. (2012), “A Robust p-spline Approach to Closed Population Capture–Recapture Models with Time Dependence and Heterogeneity,” Computational Statistics & Data Analysis, 56, 408–417. DOI: 10.1016/j.csda.2011.08.004.
   Web of Science ®Google Scholar
• Tilling, K., and Sterne, J. A. (1999), “Capture-Recapture Models Including Covariate Effects,” American Journal of Epidemiology, 149, 392–400. DOI: 10.1093/oxfordjournals.aje.a009825.
   PubMed Web of Science ®Google Scholar
• Tsiatis, A. A. (2006), Semiparametric Theory and Missing Data, New York: Springer.
   Google Scholar
• Tsybakov, A. B. (2008), Introduction to Nonparametric Estimation, New York: Springer.
   Google Scholar
• van der Laan, M. J., and Robins, J. M. (2003), Unified Methods for Censored Longitudinal Data and Causality, New York: Springer.
   Google Scholar
• van der Laan, M. J., and Rose, S. (2011), Targeted Learning: Causal Inference for Observational and Experimental Data, New York: Springer.
   Google Scholar
• van der Laan, M. J., and Rubin, D. (2006), “Targeted Maximum Likelihood Learning,” The International Journal of Biostatistics, 2, 1–40. DOI: 10.2202/1557-4679.1043.
   Google Scholar
• van der Vaart, A. (2002a), “Part III: Semiparameric Statistics,” in Lectures on Probability Theory and Statistics, ed. P. Bernard, pp. 331–457, Berlin: Springer.
   Google Scholar
• van der Vaart, A. (2014), “Higher Order Tangent Spaces and Influence Functions,” Statistical Science, 29, 679–686.
   Web of Science ®Google Scholar
• van der Vaart, A. W. (2002b), “Semiparametric Statistics,” in Lecture Notes in Mathematics (Vol. 1781), Berlin: Springer.
   Google Scholar
• Vansteelandt, S., VanderWeele, T. J., Tchetgen, E. J., and Robins, J. M. (2008), “Multiply Robust Inference for Statistical Interactions,” Journal of the American Statistical Association, 103, 1693–1704. DOI: 10.1198/016214508000001084.
   PubMed Web of Science ®Google Scholar
• Vardi, Y. (1985), “Empirical Distributions in Selection Bias Models,” The Annals of Statistics, 13, 178–203. DOI: 10.1214/aos/1176346585.
   Web of Science ®Google Scholar
• Westreich, D., and Cole, S. R. (2010), “Invited Commentary: Positivity in Practice,” American Journal of Epidemiology, 171, 674–677. DOI: 10.1093/aje/kwp436.
   PubMed Web of Science ®Google Scholar
• Wu, Y., and Yang, P. (2019), “Chebyshev Polynomials, Moment Matching, and Optimal Estimation of the Unseen,” The Annals of Statistics, 47, 857–883. DOI: 10.1214/17-AOS1665.
   Web of Science ®Google Scholar
• Yee, T. W., Stoklosa, J., and Huggins, R. M. (2015), “The VGAM Package for Capture–Recapture Data using the Conditional Likelihood,” Journal of Statistical Software, 65, 1–33. DOI: 10.18637/jss.v065.i05.
   Web of Science ®Google Scholar
• Yip, P. S., Wan, E. C., and Chan, K. S. (2001), “A Unified Approach for Estimating Population Size in Capture-Recapture Studies with Arbitrary Removals,” Journal of Agricultural, Biological, and Environmental Statistics, 6, 183–194. DOI: 10.1198/108571101750524698.
   Web of Science ®Google Scholar
• You, Y., van der Laan, M., Collender, P., Cheng, Q., Hubbard, A., Jewell, N. P., Hu, Z. T., Mejia, R., and Remais, J. (2021), “Estimation of Population Size based on Capture Recapture Designs and Evaluation of the Estimation Reliability,” arXiv preprint arXiv:2105.05373.
   Google Scholar
• Zheng, W., and van der Laan, M. J. (2010), “Asymptotic Theory for Cross-Validated Targeted Maximum Likelihood Estimation.” U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 273.
   Google Scholar
• Zwane, E., and van der Heijden, P. (2005), “Population Estimation using the Multiple System Estimator in the Presence of Continuous Covariates,” Statistical Modelling, 5, 39–52. DOI: 10.1191/1471082X05st086oa.
   Web of Science ®Google Scholar