Cator, Eric A. On the testability of the CAR assumption. (English) Zbl 1056.62003 Ann. Stat. 32, No. 5, 1957-1980 (2004). Summary: In recent years a popular nonparametric model for coarsened data is an assumption on the coarsening mechanism called coarsening at random (CAR). It has been conjectured in several papers that this assumption cannot be tested by the data, that is, the assumption does not restrict the possible distributions of the data. We show that this conjecture is not always true; an example will be current status data. We also give conditions when the conjecture is true, and in doing so, we introduce a generalized version of the CAR assumption. As an illustration, we retrieve the well-known result that the CAR assumption cannot be tested in the case of right-censored data. Cited in 1 Document MSC: 62A01 Foundations and philosophical topics in statistics 62F10 Point estimation Keywords:CAR assumption; testability; current status; bipolar theorem × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] Gill, R. D., van der Laan, M. L. and Robins, J. M. (1997). Coarsening at random: Characterisations, conjectures and counter-examples. In Proc. First Seattle Conference on Biostatistics 255–294. Springer, New York. · Zbl 0918.62003 [2] Heitjan, D. F. and Rubin, D. B. (1991). Ignorability and coarse data. Ann. Statist. 19 2244–2253. JSTOR: · Zbl 0745.62004 · doi:10.1214/aos/1176348396 [3] Jacobsen, M. and Keiding, N. (1995). Coarsening at random in general sample spaces and random censoring in continuous time. Ann. Statist. 23 774–786. JSTOR: · Zbl 0839.62001 · doi:10.1214/aos/1176324622 [4] Nielsen, S. F. (2000). Relative coarsening at random. Statist. Neerlandica 54 79–99. · Zbl 0981.62080 · doi:10.1111/1467-9574.00127 [5] Pinsker, M. S. (1964). Information and Information Stability of Random Variables and Processes . Holden–Day, San Francisco. · Zbl 0125.09202 [6] Pollard, D. (2002). A User’s Guide to Measure Theoretic Probability. Cambridge Univ. Press. · Zbl 0992.60001 · doi:10.1017/CBO9780511811555 [7] Schaefer, H. H. and Wolff, M. P. (1999). Topological Vector Spaces , 2nd ed. Springer, New York. · Zbl 0983.46002 [8] van der Vaart, A. W. (1998). Asymptotic Statistics . Cambridge Univ. Press. · Zbl 0910.62001 · doi:10.1017/CBO9780511802256 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.