Partial Identification with Proxy of Latent Confoundings via Sum-of-Ratios Fractional Programming

References

• Angrist JD, Pischke J-S (2009) Mostly Harmless Econometrics: An Empiricist’s Companion (Princeton University Press, Princeton, NJ).Google Scholar
• Balke A, Pearl J (1994) Counterfactual probabilities: Computational methods, bounds, and applications. López de Mántaras R, Poole D, eds. Proc. Tenth Conf. Uncertainty Artificial Intelligence (Morgan Kaufmann Publishers, San Mateo, CA), 46–54.Google Scholar
• Budimir I, Dragomir SS, Pečarić J (2001) Further reverse results for Jensen’s discrete inequality and applications in information theory. J. Inequality Pure Appl. Math. 2(1)5:1–14.Google Scholar
• Cai Z, Kuroki M (2012) On identifying total effects in the presence of latent variables and selection bias. Preprint, submitted June 13, https://arxiv.org/abs/1206.3239.Google Scholar
• Card D, Krueger AB (1993) Minimum wages and employment: A case study of the fast food industry in New Jersey and Pennsylvania. NBER Working Paper No. 4509, National Bureau of Economic Research, Cambridge, MA.Google Scholar
• Carroll RJ, Ruppert D, Stefanski LA, Crainiceanu CM (2006) Measurement Error in Nonlinear Models: A Modern Perspective (CRC Press, Boca Raton, FL).Google Scholar
• Castro MC, Han QC, Carvalho LR, Victora CG, França GVA (2018) Implications of Zika virus and congenital Zika syndrome for the number of live births in Brazil. Proc. Natl. Acad. Sci. USA 115(24):6177–6182.Google Scholar
• Ciarlet PG (2002) The Finite Element Method for Elliptic Problems (SIAM, Philadelphia).Google Scholar
• Cui Y, Pu H, Shi X, Miao W, Tchetgen Tchetgen E (2024) Semiparametric proximal causal inference. J. Amer. Statist. Assoc. 119(546):1348–1359.Google Scholar
• Dai Y, Shi J, Wang S (2005) Conical partition algorithm for maximizing the sum of DC ratios. J. Global Optim. 31(2):253–270.Google Scholar
• Deaner B (2018) Proxy controls and panel data. Preprint, submitted September 30, https://arxiv.org/abs/1810.00283.Google Scholar
• Du Y-J, Feng B, Fu C-H (2012) Note on cyclic sum and combination sum of color-ordered gluon amplitudes. J. High Energy Phys. 2012(1):1–23.Google Scholar
• Duarte G, Finkelstein N, Knox D, Mummolo J, Shpitser I (2024) An automated approach to causal inference in discrete settings. J. Amer. Statist. Assoc. 119(547):1778–1793.Google Scholar
• Dür M, Horst R, Thoai NV (2001) Solving sum-of-ratios fractional programs using efficient points. Optimization 49:447–466.Google Scholar
• Frost PA (1979) Proxy variables and specification bias. Rev. Econom. Statist. 61(3):323–325.Google Scholar
• Ghassami A, Shpitser I, Tchetgen Tchetgen E (2023) Partial identification of causal effects using proxy variables. Preprint, submitted April 10, https://arxiv.org/abs/2304.04374.Google Scholar
• Greenland S (2005) Multiple-bias modelling for analysis of observational data. J. Roy. Statist. Soc. Ser. A (Statist. Soc.) 168(2):267–306.Google Scholar
• Horst R, Thoai NV (1999) DC programming: Overview. J. Optim. Theory Appl. 103(1):1–43.Google Scholar
• Horst R, Pardalos PM, Van Thoai N (2000) Introduction to Global Optimization (Springer Science & Business Media, Boston).Google Scholar
• Kallus N, Mao X, Uehara M (2021) Causal inference under unmeasured confounding with negative controls: A minimax learning approach. Preprint, submitted March 25, https://arxiv.org/abs/2103.14029.Google Scholar
• Kearfott RB (1978) A proof of convergence and an error bound for the method of bisection in Rn. Math. Comput. 32:1147–1153.Google Scholar
• Kitagawa T (2009) Identification region of the potential outcome distributions under instrument independence. J. Econom. 150(2):181–193.Google Scholar
• Klee V, Minty GJ (1972) How good is the simplex algorithm. Inequalities 3:159–175.Google Scholar
• Kojima M, Mizuno S, Yoshise A (1989) A primal-dual interior point algorithm for linear programming. Megiddo N, ed. Progress in Mathematical Programming (Springer, Berlin), 29–47.Google Scholar
• Kolenikov S, Angeles G (2009) Socioeconomic status measurement with discrete proxy variables: Is principal component analysis a reliable answer? Rev. Income Wealth 55(1):128–165.Google Scholar
• Korotov S, Plaza Á, Suárez JP (2016) Longest-edge n-section algorithms: Properties and open problems. J. Comput. Appl. Math. 293:139–146.Google Scholar
• Kuroki M, Pearl J (2014) Measurement bias and effect restoration in causal inference. Biometrika 101(2):423–437.Google Scholar
• Lawler EL, Wood DE (1966) Branch-and-bound methods: A survey. Oper. Res. 14(4):699–719.Google Scholar
• Le Thi HA, Dinh TP, et al. (2014) DC programming and DCA for general DC programs. Nguyen TD, Le Thi HA, Tawfik M, eds. Advanced Computational Methods for Knowledge Engineering (Springer, Berlin), 15–35.Google Scholar
• Lee S, Bareinboim E (2020) Causal identification with matrix equations. Laboratory technical report, Columbia CausalAI, Columbia University, New York.Google Scholar
• Li A, Pearl J (2022) Bounds on causal effects and application to high dimensional data. Wooldridge ME, ed. Proc. Thirty-Sixth AAAI Conf. Artificial Intelligence, vol. 36 (AAAI Press, Palo Alto, CA), 5773–5780.Google Scholar
• Matsaglia G, Styan GPH (1974) Equalities and inequalities for ranks of matrices. Linear Multilinear Algebra 2:269–292.Google Scholar
• Miao W, Shi X, Li Y, Tchetgen Tchetgen E (2018) A confounding bridge approach for double negative control inference on causal effects. Preprint, submitted August 15, https://arxiv.org/abs/1808.04945.Google Scholar
• Miao W, Geng Z, Tchetgen Tchetgen EJ (2018) Identifying causal effects with proxy variables of an unmeasured confounder. Biometrika 105(4):987–993.Google Scholar
• Nagasawa K (2018) Identification and estimation of partial effects with proxy variables. Preprint, submitted November 1, https://arxiv.org/abs/1811.00667.Google Scholar
• Nesterov Y, Nemirovskii A (1994) Interior-Point Polynomial Algorithms in Convex Programming (SIAM, Philadelphia).Google Scholar
• Park C, Tchetgen Tchetgen E (2023) Single proxy synthetic control. Preprint, submitted July 31, https://arxiv.org/abs/2307.16353.Google Scholar
• Pearl J (2000) Models, Reasoning and Inference (Cambridge University Press, Cambridge, UK).Google Scholar
• Pearl J (2009) Causality: Models, Reasoning and Inference, 2nd ed. (Cambridge University Press, Cambridge, UK).Google Scholar
• Pearl J (2012) On measurement bias in causal inference. Preprint, submitted March 15, https://arxiv.org/abs/1203.3504.Google Scholar
• Pearl J (2013) On the testability of causal models with latent and instrumental variables. Preprint, submitted February 20, https://arxiv.org/abs/1302.4976.Google Scholar
• Pei Y, Zhu D (2013) Global optimization method for maximizing the sum of difference of convex functions ratios over nonconvex region. J. Appl. Math. Comput. 41:153–169.Google Scholar
• Rivara M-C (1984) Mesh refinement processes based on the generalized bisection of simplices. SIAM J. Numerical Anal. 21:604–613.Google Scholar
• Rothman KJ, Greenland S, Lash TL (2008) Modern Epidemiology, 3rd ed. (Lippincott Williams & Wilkins, Philadelphia).Google Scholar
• Schaible S, Shi J (2003) Fractional programming: The sum-of-ratios case. Optim. Methods Software 18:219–229.Google Scholar
• Selén J (1986) Adjusting for errors in classification and measurement in the analysis of partly and purely categorical data. J. Amer. Statist. Assoc. 81:75–81.Google Scholar
• Shen P, Zhang T, Wang C (2017) Solving a class of generalized fractional programming problems using the feasibility of linear programs. J. Inequality Appl. 2017:1–16.Google Scholar
• Shi X, Miao W, Nelson JC, Tchetgen Tchetgen EJ (2020) Multiply robust causal inference with double-negative control adjustment for categorical unmeasured confounding. J. Roy. Statist. Soc. Ser. B (Statist. Methodology) 82:521–540.Google Scholar
• Singh R (2020) Kernel methods for unobserved confounding: Negative controls, proxies, and instruments. Preprint, submitted December 18, https://arxiv.org/abs/2012.10315.Google Scholar
• Söderström T, Stoica P (2002) Instrumental variable methods for system identification. Circuits Systems Signal Processing 21:1–9.Google Scholar
• Stancu-Minasian IM (2012) Fractional Programming: Theory, Methods and Applications, vol. 409 (Springer Science & Business Media, Boston).Google Scholar
• Strand ON, Westwater ER (1968) Statistical estimation of the numerical solution of a fredholm integral equation of the first kind. J. ACM 15:100–114.Google Scholar
• Taddeo MM, Amorim LD, Aquino R (2022) Causal measures using generalized difference-in-difference approach with nonlinear models. Statist. Interface 15(4):399–413.Google Scholar
• Tao PD, An LTH (1997) Convex analysis approach to dc programming: Theory, algorithms and applications. Acta Math. Vietnam 22:289–355.Google Scholar
• Tchetgen E, Park C, Richardson D (2023) Single proxy control. Preprint, submitted February 13, https://arxiv.org/abs/2302.06054.Google Scholar
• Tchetgen EJ, Park C, Richardson DB (2024) Universal difference-in-differences for causal inference in epidemiology. Epidemiology (Fairfax) 35(1):16–22.Google Scholar
• Tchetgen EJT, Ying A, Cui Y, Shi X, Miao W (2020) An introduction to proximal causal learning. Preprint, submitted September 23, https://arxiv.org/abs/2009.10982.Google Scholar
• Wickens MR (1972) A note on the use of proxy variables. Econometrica 759–761.Google Scholar
• Wooldridge JM (2009) On estimating firm-level production functions using proxy variables to control for unobservables. Econom. Lett. 104:112–114.Google Scholar
• Xu L, Gretton A (2023) Kernel single proxy control for deterministic confounding. Preprint, submitted August 8, https://arxiv.org/abs/2308.04585.Google Scholar
• Zhang Z, Su X (2024) Partial identification with proxy of latent confoundings via sum-of-ratios fractional programming. Proc. 40th Conf. Uncertainty Artificial Intelligence, vol. 244 (PMLR, New York), 4140–4172.Google Scholar