We propose an approach for conducting inference for linear unbiased estimators applied to dependent outcomes given constraints on their independence relations, in the form of a dependency graph. We establish the consistency of an oracle variance estimator when a dependency graph is known, along with an associated central limit theorem. We derive an integer linear program for finding an upper bound for the estimated variance when a dependency graph is unknown, but topological or degree-based constraints are available on one such graph. We develop alternative bounds, including a closed-form bound, under an additional homoskedasticity assumption. We establish a basis for Wald-type confidence intervals that are guaranteed to have asymptotically conservative coverage.
Electron. J. Statist.
12(2):
2238-2252
(2018).
DOI: 10.1214/18-EJS1448
Aronow PM, Samii C (2017) Estimating average causal effects under general interference, with application to a social network experiment. Annals of Applied Statistics, 11(4):1912–1947 1383.62329 10.1214/16-AOAS1005 euclid.aoas/1514430272Aronow PM, Samii C (2017) Estimating average causal effects under general interference, with application to a social network experiment. Annals of Applied Statistics, 11(4):1912–1947 1383.62329 10.1214/16-AOAS1005 euclid.aoas/1514430272
Baldi P, Rinott Y (1989) On normal approximations of distributions in terms of dependency graphs. The Annals of Probability pp, 1646–1650 0691.60020 10.1214/aop/1176991178 euclid.aop/1176991178Baldi P, Rinott Y (1989) On normal approximations of distributions in terms of dependency graphs. The Annals of Probability pp, 1646–1650 0691.60020 10.1214/aop/1176991178 euclid.aop/1176991178
Bixby RE, Rothberg E (2007) Progress in computational mixed integer programming—a look back from the other side of the tipping point. Annals of Operations Research, 149:37–41 1213.90011 10.1007/s10479-006-0091-yBixby RE, Rothberg E (2007) Progress in computational mixed integer programming—a look back from the other side of the tipping point. Annals of Operations Research, 149:37–41 1213.90011 10.1007/s10479-006-0091-y
Chen LH, Shao QM, et al (2004) Normal approximation under local dependence. The Annals of Probability, 32(3):1985–2028 1048.60020 10.1214/009117904000000450 euclid.aop/1089808417Chen LH, Shao QM, et al (2004) Normal approximation under local dependence. The Annals of Probability, 32(3):1985–2028 1048.60020 10.1214/009117904000000450 euclid.aop/1089808417
Conley TG (1999) GMM estimation with cross sectional dependence. Journal of Econometrics, 92(1):1–45 0944.62117 10.1016/S0304-4076(98)00084-0Conley TG (1999) GMM estimation with cross sectional dependence. Journal of Econometrics, 92(1):1–45 0944.62117 10.1016/S0304-4076(98)00084-0
Crawford FW, Aronow PM, Zeng L, Li J (2017) Identification of homophily and preferential recruitment in respondent-driven sampling. American Journal of Epidemiology. In, PressCrawford FW, Aronow PM, Zeng L, Li J (2017) Identification of homophily and preferential recruitment in respondent-driven sampling. American Journal of Epidemiology. In, Press
Drton M, Richardson TS (2008) Binary models for marginal independence. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 70(2):287–309 1148.62043 10.1111/j.1467-9868.2007.00636.xDrton M, Richardson TS (2008) Binary models for marginal independence. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 70(2):287–309 1148.62043 10.1111/j.1467-9868.2007.00636.x
Hayashi F (2000) Econometrics. Princeton University Press Princeton, NJ 0994.62107Hayashi F (2000) Econometrics. Princeton University Press Princeton, NJ 0994.62107
Horvitz DG, Thompson DJ (1952) A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association, 47(260):663–685 MR0053460 10.1080/01621459.1952.10483446Horvitz DG, Thompson DJ (1952) A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association, 47(260):663–685 MR0053460 10.1080/01621459.1952.10483446
Kellerer H, Pferschy U, Pisinger D (2004a) Introduction to NP-Completeness of knapsack problems., Springer 1103.90003Kellerer H, Pferschy U, Pisinger D (2004a) Introduction to NP-Completeness of knapsack problems., Springer 1103.90003
Liang KY, Zeger SL (1986) Longitudinal data analysis using generalized linear models. Biometrika pp, 13–22 0595.62110 10.1093/biomet/73.1.13Liang KY, Zeger SL (1986) Longitudinal data analysis using generalized linear models. Biometrika pp, 13–22 0595.62110 10.1093/biomet/73.1.13
Linderoth JT, Lodi A (2010) MILP software. In: Cochran JJ, Cox LA, Keskinocak P, Kharoufeh JP, Smith JC (eds) Wiley Encyclopedia of Operations Research and Management Science, WileyLinderoth JT, Lodi A (2010) MILP software. In: Cochran JJ, Cox LA, Keskinocak P, Kharoufeh JP, Smith JC (eds) Wiley Encyclopedia of Operations Research and Management Science, Wiley
Liu L, Hudgens MG (2014) Large sample randomization inference of causal effects in the presence of interference. Journal of the American Statistical Association, 109(505):288–301 1367.62239 10.1080/01621459.2013.844698Liu L, Hudgens MG (2014) Large sample randomization inference of causal effects in the presence of interference. Journal of the American Statistical Association, 109(505):288–301 1367.62239 10.1080/01621459.2013.844698
Neyman J (1923 [1990]) On the application of probability theory to agricultural experiments. Essay on principles. Section 9. Reprinted in Statist. Sci., 5:465–472 0955.01560 10.1214/ss/1177012031 euclid.ss/1177012031Neyman J (1923 [1990]) On the application of probability theory to agricultural experiments. Essay on principles. Section 9. Reprinted in Statist. Sci., 5:465–472 0955.01560 10.1214/ss/1177012031 euclid.ss/1177012031
Ogburn EL, VanderWeele TJ, et al (2017) Vaccines, contagion, and social networks. The Annals of Applied Statistics, 11(2):919–948 1391.62237 10.1214/17-AOAS1023 euclid.aoas/1500537729Ogburn EL, VanderWeele TJ, et al (2017) Vaccines, contagion, and social networks. The Annals of Applied Statistics, 11(2):919–948 1391.62237 10.1214/17-AOAS1023 euclid.aoas/1500537729
Overton WS, Stehman SV (1995) The horvitz-thompson theorem as a unifying perspective for probability sampling: with examples from natural resource sampling. The American Statistician, 49(3):261–268Overton WS, Stehman SV (1995) The horvitz-thompson theorem as a unifying perspective for probability sampling: with examples from natural resource sampling. The American Statistician, 49(3):261–268
Richardson T (2003) Markov properties for acyclic directed mixed graphs. Scandinavian Journal of Statistics, 30(1):145–157 1035.60005 10.1111/1467-9469.00323Richardson T (2003) Markov properties for acyclic directed mixed graphs. Scandinavian Journal of Statistics, 30(1):145–157 1035.60005 10.1111/1467-9469.00323
Tabord-Meehan M (2015) Inference with dyadic data: Asymptotic behavior of the dyadic-robust t-statistic. arXiv preprint, arXiv:1510.07074Tabord-Meehan M (2015) Inference with dyadic data: Asymptotic behavior of the dyadic-robust t-statistic. arXiv preprint, arXiv:1510.07074