References
- Deville JC, Särndal CE. Calibration estimators in survey sampling. J Amer Statist Assoc. 1992;87:376–382. doi: 10.1080/01621459.1992.10475217
- Horvitz DG, Thompson DJ. A generalization of sampling without replacement from a finite universe. J Amer Statist Assoc. 1953;47:663–685. doi: 10.1080/01621459.1952.10483446
- Särndal CE, Swensson B, Wretman J. Model assisted survey sampling. Springer Series in Statistics. New York: Springer; 1992.
- Montanari GE, Ranalli MG. Nonparametric model calibration estimation in survey sampling. J Amer Statist Assoc. 2005;100:1429–1442. doi: 10.1198/016214505000000141
- Rao JNK, Kovar JG, Mantel HJ. On estimating distribution functions and quantiles from survey data using auxiliary information. Biometrika. 1990;77:365–375. doi: 10.1093/biomet/77.2.365
- Kovaĉević M. Calibration estimation of cumulative distribution and quantile functions from survey data. Proceedings of the Survey Methods Section, Statistical Society of Canada; 1997;47:139–144.
- Théberge A. Extensions of calibration estimators in survey sampling. J Amer Statist Assoc. 1999;94:635–644.
- Singh S. Generalized calibration approach for estimating variance in survey sampling. Ann Inst Statist Math. 2001;53:404–417. doi: 10.1023/A:1012431008950
- Wu C, Sitter RR. A model-calibration approach to using complete auxiliary information from survey data. J Amer Statist Assoc. 2001;96:185–193. doi: 10.1198/016214501750333054
- Wu C. Optimal calibration estimators in survey sampling. Biometrika. 2003;90:937–951. doi: 10.1093/biomet/90.4.937
- Harms T, Duchesne P. On calibration estimation for quantiles. Surv Methodol. 2006;32:37–52.
- Rueda M, Martínez S, Martínez H, Arcos A. Estimation of the distribution function with calibration methods. J Statist Plann Inference. 2007;137:435–448. doi: 10.1016/j.jspi.2005.12.011
- Särndal CE. The calibration approach in survey theory and practice. Surv Methodol. 2007;33:99–119.
- Breidt FJ, Opsomer JD. Local polynomial regression estimators in survey sampling. Ann Statist. 2000;28:1026–1053. doi: 10.1214/aos/1015956706
- Chaouch M, Goga C. Using complex surveys to estimate the l1-median of a functional variable: application to electricity load curves. Int Stat Rev. 2012;80:40–59. doi: 10.1111/j.1751-5823.2011.00172.x
- Ramsay JO, Silverman BW. Applied functional data analysis: methods and case studies. New York: Springer-Verlag; 2002.
- Ramsay JO, Silverman BW. Functional data analysis. 2nd ed. Springer Series in Statistics. New York: Springer-Verlag; 2005.
- Horváth L, Kokoszka P. Inference for functional data with applications. Springer Series in Statistics. New York: Springer; 2012.
- Cardot H, Josserand E. Horvitz–Thompson estimators for functional data: asymptotic confidence bands and optimal allocation for stratified sampling. Biometrika. 2011;98:107–118. doi: 10.1093/biomet/asq070
- Cardot H, Degras D, Josserand E. Confidence bands for Horvitz–Thompson estimators using sampled noisy functional data; 2011. ArXiv:1105.2135v1. Available from: http://arxiv.org/abs/1105.2135v1.
- Gamboa F, Loubes J-M, Rochet P. Maximum entropy estimation for survey sampling. J Statist Plann Inference. 2011;141:305–317. doi: 10.1016/j.jspi.2010.06.002
- Gzyl H, Velásquez Y. Linear inverse problems: the maximum entropy connection, volume 83 of series on Advances in mathematics for applied sciences. Singapore: World Scientific; 2011.
- Navaza J. On the maximum entropy estimate of electron density function. Acta Crystallogr. 1985;A41:232–244. doi: 10.1107/S0108767385000526
- Navaza J. The use of non-local constraints in maximum-entropy electron density reconstruction. Acta Crystallogr. 1986;A42:212–223. doi: 10.1107/S0108767386099397
- Gamboa F. Méthode du maximum d'entropie sur la moyenne et applications [PhD thesis]. Université de Paris-Sud, Orsay; 1989.
- Dacunha-Castelle D, Gamboa F. Maximum d'entropie et problème des moments. Ann Inst H Poincaré Probab Statist. 1990;26:567–596.
- Gamboa F, Gassiat E. Bayesian methods and maximum entropy for ill-posed inverse problems. Ann Statist. 1997;25:328–350. doi: 10.1214/aos/1034276632
- Csiszár I, Gamboa F, Gassiat E. MEM pixel correlated solutions for generalized moment and interpolation problems. IEEE Trans Inform Theory. 1999;45(7):2253–2270. doi: 10.1109/18.796367
- Mohammad-Djafari A. A comparison of two approaches: maximum entropy on the mean (MEM) and Bayesian estimation (BAYES) for inverse problems. In: Sears M, Nedeljkovic V, Pendock NE, Sibisi S, editors. Maximum entropy and Bayesian methods. Berg-en-Dal, South Africa: Kluwer Academic Publishers; 1996, p. 77–91.
- Maréchal P. On the principle of maximum entropy as a methodology for solving linear inverse problems. In: Grigelionis B, Kubilius VPJ, Pragarauskas H, Ruszkis R, Statulevicius V, editors. Probability theory and mathematical statistics. Proceedings of the Seventh Vilnius Conference. Vilnius, Lithuania: VPS/TEV; 1999. p. 481–492.
- Gzyl H. Maxentropic reconstruction of some probability distributions. Stud Appl Math. 2000;105:235–243. doi: 10.1111/1467-9590.00150
- Golan A, Gzyl H. An entropic estimator for linear inverse problems. Entropy. 2012;14:892–923. doi: 10.3390/e14050892
- Fermín AK, Loubes J-M, Ludeña C. Bayesian methods for a particular inverse problem: seismic tomography. Int J Tomogr Stat. 2006;4(W06):1–19.
- Csiszár I. I-divergence geometry of probability distributions and minimization problems. Ann Probab. 1975;3:146–158. doi: 10.1214/aop/1176996454
- Kress R. Linear integral equations, volume 82 of applied mathematical sciences. 2nd ed. New York: Springer-Verlag; 1999.
- Csiszár I. Sanov property, generalized I-projection and a conditional limit theorem. Ann Probab. 1984;12:768–793. doi: 10.1214/aop/1176993227
- Varadhan R. R-package BB: solving and optimizing large-scale nonlinear systems; 2012. Available from: http://cran.r-project.org.
- Varadhan R, Gilbert P. BB: An R package for solving a large system of nonlinear equations and for optimizing a high-dimensional nonlinear objective function. J Statist Softw. 2009;32. Available from: http://www.jstatsoft.org/v32/i04/.
- Fuller WA. Sampling statistics. Wiley Series in Survey Methodology. Hoboken (NJ): Wiley; 2009.