On the impact of robust statistics on imprecise probability models: A review

Structural Safety

Volumn 32, Issue 6, 2010, Pages 358-365

  Augustin, Thomas ^a   Hable, Robert ^b  

^a UNIVERSITY OF MUNICH   (Germany)

^b UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

Hypotheses testing; Imprecise probabilities; Interval probability; Neighborhood models; Parameter estimation; Robust statistics; Sensitivity analysis; Statistical analysis

Indexed keywords

HYPOTHESES TESTING; IMPRECISE PROBABILITIES; INTERVAL PROBABILITY; NEIGHBORHOOD MODEL; ROBUST STATISTICS; STATISTICAL ANALYSIS;

PARAMETER ESTIMATION; PROBABILISTIC LOGICS; PROBABILITY DENSITY FUNCTION; SENSITIVITY ANALYSIS; STATISTICS; STOCHASTIC MODELS;

PROBABILITY;

EID: 77957587420     PISSN: 01674730     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.strusafe.2010.06.002     Document Type: Article

References (132)

1. Corotis R.B. Risk communication with generalized uncertainty and linguistics. Struct Saf 2009, 31(2):113-117.
2. Oberguggenberger M., Schueller G., Marti K. Special issue on fuzzy sets, imprecise probability, and stochastic engineering. ZAMM J Appl Math Mech 2004, 84(10-11):661-776.
3. Moeller B., Beer M. Engineering computation under uncertainty - capabilities of non-traditional models. Comput Struct 2008, 86(10):1024-1041.
4. Oberguggenberger M. Introductory remarks: mathematical models of uncertainty. ZAMM J Appl Math Mech 2004, 84(10-11):661-665.
5. Aughenbaugh J.M., Paredis C.J.J. The value of using imprecise probabilities in engineering design. ASME J Mech Des 2006, 128(4):969-979.
6. Analyzing uncertainty in civil engineering 2005, Springer, Berlin. W. Fellin, H. Lessmann, M. Oberguggenberger, R. Vieider (Eds.).
7. Utkin L.V., Coolen F.P.A. Imprecise reliability: an introductory overview. Neural and fuzzy techniques in reliability 2007, vol. 2:261-306. Springer. G. Levitin (Ed.).
8. Oberguggenberger M., King J., Schmelzer B. Imprecise probability methods for sensitivity analysis in engineering. Int J Approx Reason 2009, 50:680-693.
9. Zhang M., Beer M., Quek S., Choo Y. Comparison of uncertainty models in reliability analysis of offshore structures under marine corrosion. Struct Saf 2010, 32(6):425-432.
10. Ferson S., Tucker W.T. Sensitivity analysis using probability bounding. Reliab Eng Syst Saf 2006, 91:1443-1451.
11. Hall J.W. Uncertainty-based sensitivity indices for imprecise probability distributions. Reliab Eng Syst Saf 2006, 91:1443-1451.
12. Tonon F., Bernardini A., Mammino A. Determination of parameters range in rock engineering by means of random set theory. Reliab Eng Syst Saf 2000, 70:241-261.
13. Oberguggenberger M., Fellin W. Reliability bounds through random sets: non-parametric methods and geotechnical applications. Comput Struct 2008, 86(10):1093-1101.
14. Fuchs M., Neumaier A. Potential based clouds in robust design optimization. J Stat Theory Practice 2008, 3(1):225-238. [reprinted in [19]].
15. Huber P. The use of Choquet capacities in statistics. In: Proceedings of the 39th session of the International Statistical Institute. Bulletin de l'Institut International de Statistique 45, book 4; 1973. p. 181-91.
16. Huber P.J. Kapazitäten statt Wahrscheinlichkeiten? Gedanken zur Grundlegung der Statistik. Jber Deutsch Math-Verein 1976/77, 78(2):81-92.
17. De Cooman G, Vejnarovn J, Zaffalon M, editors. ISIPTA '07. Proceedings of the fifth international symposium on imprecise probability: theories and applications. Charles Univ., Prague, SIPTA, Manno; 2007.
18. Soft methods for handling variability and imprecision (advances in intelligent and soft computing) 2008, Springer. D. Dubois, M. Lubiano, H. Prade, M. Gil, P. Grzegorzewski, O. Hryniewicz (Eds.).
19. Special issue on statistical theory and practice with imprecison. Journal of Statistical Theory and Practice 2009, 3(1):1-303. reprinted with journal editor Sat Gupta as further editor: Imprecision in Statistical Theory and Practice. Grace, Greensboro.
20. Augustin T, Coolen F, Moral S, Troffaes M, editors. ISIPTA '09. Proceedings of the sixth international symposium on imprecise probability: theories and applications, Durham, UK, SIPTA, Manno; 2009. http://www.sipta.org/isipta09/proceedings/.
21. Walley P. Towards a unified theory of imprecise probability. Int J Approx Reason 2000, 24(2-3):125-148.
22. Weichselberger K. The theory of interval-probability as a unifying concept for uncertainty. Int J Approx Reason 2000, 24(2-3):149-170.
23. Weichselberger K. Elementare Grundbegriffe einer allgemeineren Wahrscheinlichkeitsrechnung. I. Intervallwahrscheinlichkeit als umfassendes Konzept 2001, Physica, Heidelberg.
24. Walley P. Statistical reasoning with imprecise probabilities 1991, Chapman & Hall, London.
25. Huber P.J., Strassen V. Minimax tests and the Neyman-Pearson lemma for capacities. Ann Stat 1973, 1:251-263.
26. Shafer G. A mathematical theory of evidence 1976, Princeton University Press, Princeton.
27. Rieder H. Robust asymptotic statistics 1994, Springer, New York.
28. Hafner R. Construction of minimax-tests for bounded families of distribution-functions. Contributions to stochastics (Festschrift for Walther Eberl) 1987, 145-152. Physica, Heidelberg. W. Sendler (Ed.).
29. Hafner R. Konstruktion robuster Teststrategien. Data analysis and statistical inference (Festschrift for Friedhelm Eicker) 1992, 145-160. Eul, Bergisch Gladbach. S. Schach, G. Trenkler (Eds.).
30. Berleant D., Zhang J. Representation and problem solving with the distribution envelope determination (denv) method. Reliab Eng System Saf 2004, 153-168.
31. Ferson S, Kreinovich V, Ginzburg L, Myers DS, Sentz K. Constructing probability boxes and Dempster-Shafer structures. Technical report SAND2007-0939, Sandia National Laboratories; 2003.
32. Destercke S., Dubois D., Chojnacki E. Unifying practical uncertainty representations - I: generalized p-boxes. Int J Approx Reason 2008, 49(3):649-663.
33. Destercke S, Dubois D. The role of generalised p-boxes in imprecise probability models. In: Augustin T, Coolen F, Moral S, Troffaes M, editors. ISIPTA '09. Proceedings of the sixth international symposium on imprecise probability: theories and applications, Durham, UK, SIPTA, Manno; 2009. p. 179-88. http://www.sipta.org/isipta09/proceedings/.
34. Berger J. Robust Bayesian analysis: sensitivity to the prior. J Stat Plan Infer 1990, 25(3):303-328.
35. Weichselberger K., Pöhlmann S. A methodology for uncertainty. Lecture notes in artificial intelligence 1990, vol. 419. Springer-Verlag, Heidelberg.
36. Tessem B. Interval probability propagation. Int J Approx Reason 1992, 7(3-4):95-120.
37. de Campos L.M., Huete J.F., Moral S. Probability intervals: a tool for uncertain reasoning. Int J Uncertain, Fuzz Knowledge-Based Syst 1994, 2:167-196.
38. Huber P. Robust statistics 1981, John Wiley & Sons Inc., New York.
39. Hampel F. Nonadditive probabilities in statistics. J Statis Theory Pract 2009, 3(1):11-23. [reprinted in [19]].
40. Moreno E. Global Bayesian robustness for some classes of prior distributions. Lecture notes in statistics 2000, vol. 152:45-70. Springer, New York. D.R. Insua, F. Ruggeri (Eds.).
41. Shyamalkumar N. Likelihood robustness. Lecture notes in statistics 2000, vol. 152:127-143. Springer, New York. D.R. Insua, F. Ruggeri (Eds.).
42. Rieder H. Least favorable pairs for special capacities. Ann Stat 1977, 5:909-921.
43. Birgé L. Tests robustes pour des variables indépendantes et des chai{dotless}̂ nes de Markov. Ann Sci Univ Clermont-Ferrand II. Math 1982, 20:70-77.
44. Huber C. Théorie de la robustesse. Lecture notes in mathematics 1986, vol. 1215:1-128. Springer, Berlin.
45. Walley P., Fine T.L. Towards a frequentist theory of upper and lower probability. Ann Stat 1982, 10(3):741-761.
46. Couso I., Moral S., Walley P. A survey of concepts of independence for imprecise probabilities. Risk Decis Policy 2000, 5:165-181.
47. de Cooman G, Hermans F, Antonucci A, Zaffalon M. Epistemic irrelevance in credal networks: the case of imprecise markov trees. In: Augustin T, Coolen FPA, Moral S, Troffaes MCM, editors. ISIPTA '09. Proceedings of the sixth international symposium on imprecise probabilities: theories and applications, Durham, UK, SIPTA, Manno; 2009. p. 149-58 [extended version to appear in International Journal of Approximate Reasoning]. http://www.sipta.org/isipta09/proceedings/.
48. Troffaes M. Decision making under uncertainty using imprecise probabilities. Int J Approx Reason 2007, 45:17-29.
49. Augustin T. Neyman-Pearson testing under interval probability by globally least favorable pairs reviewing Huber-Strassen theory and extending it to general interval probability. J Stat Plan Infer 2002, 105(1):149-173.
50. Wallner A. Bi-elastic neighbourhood models. In: Bernard J-M, Seidenfeld T, Zaffalon M, editors. ISIPTA '03. Proceedings of the third international symposium on imprecise probabilities and their applications, Lugano, Carleton Scientific; 2005. p. 593-607. http://www.sipta.org/isipta03/proceedings/.
51. Skulj D. Generalized conditioning in neighbourhood models. In: ISIPTA '05. Proceedings of the fourth international symposium on imprecise probabilities and their applications, CMU, Pittsburgh, SIPTA, Manno; 2005. p. 322-31. http://www.sipta.org/isipta05/proceedings/.
52. Škulj D. Jeffrey's conditioning rule in neighbourhood models. Int J Approx Reason 2006, 42(3):192-211.
53. Bednarski T. On solutions of minimax test problems for special capacities. Z Wahrscheinlichkeitstheorie und Verw Gebiete 1981, 58(3):397-405.
54. Buja A. On the Huber-Strassen theorem. Probab Theory Relat Fields 1986, 73(1):149-152.
55. Österreicher F. On the construction of least favourable pairs of distributions. Z Wahrscheinlichkeitstheorie und Verw Gebiete 1978, 43(1):49-55.
56. Hafner R. Simple construction of least favourable pairs of distributions and of robust tests for Prokhorov-neighbourhoods. Math Operationsforsch Statist Ser Statist 1982, 13(1):33-46.
57. Hafner R. Construction of minimax-tests for bounded families of probability-densities. Metrika 1993, 40(1):1-23.
58. Augustin T. Optimale tests bei intervallwahrscheinlichkeit 1998, Vandenhoeck & Ruprecht, Göttingen.
59. Obermeier M, Augustin T. Lucenos discretization method and its application in decision making under ambiguity. In: de Cooman G, Vejnarová J, Zaffalon M, editors. ISIPTA '07. Proceedings of the fifth international symposium on imprecise probability: theories and applications (Charles Univ., Prague), SIPTA, Manno; 2007. p. 327-36. http://www.sipta.org/isipta07/proceedings/>.
60. Hable R. Finite approximations of data-based decision problems under imprecise probabilities. Int J Approx Reason 2009, 50:1115-1128.
61. Bednarski T. On extension of the Neyman-Pearson lemma for capacities to dependent random variables. Statistics 1986, 17(4):549-556.
62. Rieder H. A robust asymptotic testing model. Ann Stat 1978, 6(5):1080-1094.
63. Bednarski T. A robust asymptotic testing model for special capacities. Statistics 1985, 16(4):507-519.
64. Bednarski T. Binary experiments, minimax tests and 2-alternating capacities. Ann Stat 1982, 10(1):226-232.
65. Lembcke J. The necessity of strongly subadditive capacities for Neyman-Pearson minimax tests. Monatsh Math 1988, 105(2):113-126.
66. Schied A. Optimal investments for robust utility functionals in complete market models. Math Oper Res 2005, 30(3):750-764.
67. Augustin T. On data-based checking of hypotheses in the presence of uncertain knowledge. Classification in the information age, studies in classification, data analysis and knowledge organization 1999, 127-135. Springer. W. Gaul, H. Locarek-Junge (Eds.).
68. Baumann V. Eine parameterfreie Theorie der ungünstigsten Verteilungen für das Testen von Hypothesen. Z Wahrscheinlichkeitstheorie und Verw Gebiete 1968, 11:41-60.
69. Plachky D., Rüschendorf L. Conservation of the UMP-resp. maximin-property of statistical tests under extensions of probability measures. Colloquia Mathematica Societatis Janos Bolyai 1987, vol. 45:439-457. North-Holland, Amsterdam.
70. Rüschendorf L. Robust tests against dependence. Probab Math Stat 1985, 6(1):1-10.
71. Bronevich A, Augustin T. Approximation of coherent lower probabilities by 2-monotone measures. In: Augustin T, Coolen F, Moral S, Troffaes M, editors. ISIPTA '09. Proceedings of the sixth international symposium on imprecise probabilities: theories and applications (Durham, UK), SIPTA, Manno; 2009. p. 61-9. http://www.sipta.org/isipta09/proceedings/>.
72. Augustin T. On decision making under ambiguous prior and sampling information. In: Cooman GD, Fine T, Seidenfeld T, editors. ISIPTA '01. Proceedings of the second international symposium on imprecise probabilities and their applications (Cornell Univ., Ithaca, NY), Shaker, Maastricht; 2001. p. 9-16. http://www.sipta.org/isipta01/proceedings/>.
73. Augustin T. Optimal decisions under complex uncertainty-basic notions and a general algorithm for data-based decision making with partial prior knowledge described by interval probability. ZAMM J Appl Math Mech 2004, 84(10-11):678-687.
74. Utkin L, Augustin T. Powerful algorithms for decision making under partial prior information and general ambiguity attitudes. In: Cozman F, Nau R, Seidenfeld T, editors. ISIPTA '05. Proceedings of the fourth international symposium on imprecise probabilities and their applications (CMU, Pittsburgh), SIPTA, Manno; 2005. p. 349-58. http://www.sipta.org/isipta05/proceedings/>.
75. Kikuti D, Cozman F, de Campos C. Partially ordered preferences in decision trees: computing strategies with imprecision in probabilities. In: Brafman R, Junker U, editors. Multidisciplinary IJCAI-05 workshop on advances in preference handling (Edinburgh); 2005. p. 118-23. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.60.1872&rep =rep1&type=pdf>type=pdf.
76. Hable R. Data-based decisions under complex uncertainty. PhD thesis, Ludwig-Maximilians-Universität (LMU) Munich; 2009. http://edoc.ub.uni-muenchen.de/9874/>.
77. Hable R. Data-based decisions under imprecise probability and least favorable models. Int J Approx Reason 2009, 50:642-654.
78. Buja A. Simultaneously least favorable experiments. I. Upper standard functionals and sufficiency. Z Wahrscheinlichkeitstheorie und Verw Gebiete 1984, 65(3):367-384.
79. Huber P. Robust confidence limits. Z Wahrscheinlichkeitstheorie und Verw Gebiete 1968, 10:269-278.
80. Rieder H. A finite-sample minimax regression estimator. Statistics 1989, 20(2):211-221.
81. Rieder H. Robustness in structured models. Grundlagen der Statistik und ihre Anwendungen (Festschrift for Kurt Weichselberger) 1995, 172-187. Physika-Verlag, Heidelberg. H. Rinne, B. Rüger, H. Strecker (Eds.).
82. Kohl M. Numerical contributions to the asymptotic theory of robustness. PhD thesis, Universität Bayreuth; 2005. http://opus.ub.uni-bayreuth.de/volltexte/2006/195/pdf/DissMKohl.pdf>.
83. Hable R. A minimum distance estimator in an imprecise probability model: computational aspects and applications. In: Augustin T, Coolen F, Moral S, Troffaes M, editors. ISIPTA '09. Proceedings of the sixth international symposium on imprecise probability: theories and applications (Durham, UK), SIPTA, Manno; 2009. p. 209-18 [extended version to appear in International Journal of Approximate Reasoning]. http://www.sipta.org/isipta09/proceedings/>.
84. Hable R. Minimum distance estimation in imprecise probability models. J Stat Plan Infer 2010, 140:461-479.
85. Hable R. imprProbEst: minimum distance estimation in an imprecise probability model, contributed R-Package on CRAN, Version 1.0, 2008-10-23; maintainer Hable, R.; 2008.
86. Millar P. Robust estimation via minimum distance methods. Z Wahrscheinlichkeitstheorie und Verw Gebiete 1981, 55(1):73-89.
87. Donoho D., Liu R. The " automatic" robustness of minimum distance functionals. Ann Stat 1988, 16(2):552-586.
88. Öztürk Ö., Hettmansperger T. Simultaneous robust estimation of location and scale parameters: a minimum-distance approach. Can J Stat 1998, 26(2):217-229.
89. Hampel F., Ronchetti E., Rousseeuw P., Stahel W. Robust statistics 1986, John Wiley & Sons Inc., New York.
90. Jurečková J., Sen P. Robust statistical procedures 1996, John Wiley & Sons Inc., New York.
91. Maronna R., Martin D., Yohai V. Robust statistics 2006, John Wiley & Sons Ltd., Chichester.
92. De Cooman G., Miranda E. Weak and strong laws of large numbers for coherent lower previsions. J Stat Plan Infer 2008, 138(8):2409-2432.
93. Cozman F. Concentration inequalities and laws of large numbers under epistemic irrelevance. In: Augustin T, Coolen F, Moral S, Troffaes M, editors. ISIPTA '09. Proceedings of the sixth international symposium on imprecise probabilities: theories and applications (Durham, UK), SIPTA, Manno; 2009. p. 109-18 [extended version to appear in International Journal of Approximate Reasoning]. http://www.sipta.org/isipta09/proceedings/>.
94. Bickel P. Quelques aspects de la statistique robuste. Ecole d'ete de probabilites de Saint-Flour IX-1979, Lect. Notes Math. 1981, 876:2-72.
95. Ruckdeschel P. A motivation for 1/n-shrinking neighborhoods. Metrika 2006, 63:295-307.
96. Kohl M, Ruckdeschel P. ROptEst: optimally robust estimation, contributed R-Package on CRAN, Version 0.6.0, 2008-08-07; maintainer Kohl, M.; 2008.
97. Walley P. Inferences from multinomial data: learning about a bag of marbles. J Roy Stat Soc Ser B (Statistical Methodology) 1996, 58:3-57.
98. Quaeghebeur E, de Cooman G. Imprecise probability models for inference in exponential families. In: Cozman F, Nau R, Seidenfeld T, editors. ISIPTA '05. Proceedings of the fourth international symposium on imprecise probabilities and their applications (CMU, Pittsburgh), SIPTA, Manno; 2005. p. 287-96. http://www.sipta.org/isipta05/proceedings/>.
99. Walter G, Augustin T, Peters A. Linear regression analysis under sets of conjugate priors. In: De Cooman G, Vejnarova J, Zaffalon M, editors. ISIPTA '07. Proceedings of the fifth international symposium on imprecise probability: theories and applications (Charles Univ., Prague), SIPTA, Manno; 2007. p. 445-64. http://www.sipta.org/isipta07/proceedings/>.
100. Utkin L., Augustin T. Decision making under incomplete data using the imprecise Dirichlet model. Int J Approx Reason 2007, 44(3):322-338.
101. Walter G., Augustin T. Imprecision and prior-data conflict in generalized Bayesian inference. J Stat Theory Pract 2009, 3:255-271.
102. Augustin T. On the suboptimality of the generalized Bayes rule and robust Bayesian procedures from the decision theoretic point of view: a cautionary note on updating imprecise priors. In: Bernard J, Seidenfeld T, Zaffalon M, editors. ISIPTA '03. Proceedings of the third international symposium on imprecise probabilities and their applications (Lugano), Carleton Scientific, Waterloo; 2003. p. 31-45. http://www.sipta.org/isipta03/proceedings//>.
103. Ferson S., Ginzburg L., Kreinovich V., Longpré L., Aviles M. Exact bounds on finite populations of interval data. Reliable Comput 2001, 11:207-233.
104. Ferson S, Kreinovich V, Hajagos J, Oberkampf W, Ginzburg L. Experimental uncertainty estimation and statistics for data having interval uncertainty. Technical report SAND2002-4015, Sandia National Laboratories; January 2007.
105. Rohwer G., Pötter U. Grundzüge der sozialwissenschaftlichen Statistik 2001, Juventa, Weinheim.
106. Symbolic data analysis and the SODAS software 2008, John Wiley & Sons. E. Diday, M. Noirhomme-Freiture (Eds.).
107. de Cooman G., Zaffalon M. Updating beliefs with incomplete observations. Artif Int 2004, 159:75-125.
108. Zaffalon M., Miranda E. Conservative inference rule for uncertain reasoning under incompleteness. J Artif Intell Res 2009, 34:757-821.
109. Manski C. Partial identification of probability distributions 2003, Springer, New York.
110. Manski C. Partial identification with missing data: concepts and findings. Int J Approx Reason 2005, 39(2-3):151-165.
111. Manski C.F. Identification for prediction and decision 2009, Harvard University Press, Cambridge (MA).
112. Blundell R., Browning M., Crawford I. Best nonparametric bounds on demand responses. Econometrica 2008, 76(6):1227-1262.
113. Gundersen C., Kreider B. Bounding the effects of food insecurity on children's health outcomes. J Health Econ 2009, 28(5):971-983.
114. Kreider B., Hill S. Partially identifying treatment effects with an application to covering the uninsured. J Hum Resour 2009, 44(2):409-449.
115. Manski C., Pepper J. More on monotone instrumental variables. Econom J 2009, 12:200-216.
116. Stoye J. Partial identification and robust treatment choice: an application to young offenders. J Stat Theory Pract 2009, 3(1):239-254. reprinted in [19].
117. Imbens G., Manski C. Confidence intervals for partially identified parameters. Econometrica 2004, 72(6):1845-1857.
118. Stoye J. More on confidence intervals for partially identified parameters. Econometrica 2009, 77(4):1299-1315.
119. Zhang Z. Likelihood-based confidence sets for partially identified parameters. J Stat Plan Infer 2009, 139(3):696-710.
120. Vansteelandt S., Goetghebeur E., Kenward M.G., Molenberghs G. Ignorance and uncertainty regions as inferential tools in a sensitivity analysis. Stat Sin J Stat Theory Pract 2006, 16(3):953-979.
121. Gustafson P., Greenland S. Interval estimation for messy observational data. Stat Sci 2009, 24(3):328-342.
122. Cheng J., Small D. Bounds on causal effects in three-arm trials with non-compliance. J Roy Stat Soc Ser B (Statistical Methodology) 2006, 68(5):815-836.
123. Copas J., Jackson D. A bound for publication bias based on the fraction of unpublished studies. Biometrics 2004, 60(1):146-153.
124. Henmi M., Copas J.B., Eguchi S. Confidence intervals and P-values for meta-analysis with publication bias. Biometrics 2007, 63(2):475-482.
125. Lyles R.H., Allen A.S., Flanders W.D., Kupper L.L., Christensen D.L. Inference for case-control studies when exposure status is both informatively missing and misclassified. Stat Med 2006, 25(23):4065-4080.
126. Molenberghs G. Incomplete data in clinical studies: analysis, sensitivity, and sensitivity analysis. Drug Inf J 2009, 43(4):409-429.
127. Steenland K., Greenland S. Monte Carlo sensitivity analysis and Bayesian analysis of smoking as an unmeasured confounder in a study of silica and lung cancer. Am J Epidemiol 2004, 160(4):384-392.
128. McCandless L.C., Gustafson P., Levy A. Bayesian sensitivity analysis for unmeasured confounding in observational studies. Stat Med 2007, 26(11):2331-2347.
129. McCandless L.C., Gustafson P., Levy A.R. A sensitivity analysis using information about measured confounders yielded improved uncertainty assessments for unmeasured confounding. J Clin Epidemiol 2008, 61(3):247-255.
130. Beunckens C., Sotto C., Molenberghs G., Verbeke G. A multifaceted sensitivity analysis of the Slovenian public opinion survey data. J Roy Stat Soc Ser C (Applied Statistics). Part 2 2009, 58:171-196. Corr: 575-576.
131. Molinari F. Partial identification of probability distributions with misclassified data. J Econom 2008, 144(1):81-117.
132. Kunz A, Augustin T, Küchenhoff H. Partially identified prevalence estimation under misclassification using the kappa coefficient. Technical report no. 74, Department of Statistics, University of Munich (LMU); 2010 http://epub.ub.uni-muenchen.de/11324/1/tr074.pdf>.