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    A note on multiple imputation for method of moments estimation

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    Multiple imputation is widely used for estimation in situations where there are missing data. Rubin (1987) provided an easily applicable formula for multiple imputation variance estimation, but its validity requires the congeniality condition of Meng (1994), which may not be satisfied for method of moments estimation. We give the asymptotic bias of Rubin's variance estimator when method of moments estimation is used in the complete-sample analysis for each imputed dataset. A new variance estimator based on over-imputation is proposed to provide asymptotically valid inference in this case.This is a pre-copyedited, author-produced PDF of an article accepted for publication in Biometrika following peer review. The version of record (S. Yang, J. K. Kim; A note on multiple imputation for method of moments estimation. Biometrika 2016; 103 (1): 244-251) is available online at doi:10.1093/biomet/asv073. Posted with permission.</p

    Yang-Baxter maps and the discrete KP hierarchy

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    We present a systematic construction of the discrete KP hierarchy in terms of Sato–Wilson-type shift operators. Reductions of the equations in this hierarchy to 1+1-dimensional integrable lattice systems are considered, and the problems that arise with regard to the symmetry algebra underlying the reduced systems as well as the ultradiscretizability of these systems are discussed. A scheme for constructing ultradiscretizable reductions that give rise to Yang–Baxter maps is explained in two explicit examples
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