This paper deals with the relatively new field of sequencebased estimation which involves utilizing both the information in the observations and in their sequence of appearance. Our intention is to obtain Maximum Likelihood estimates by “extracting” the information contained in the observations when perceived as a sequence rather than as a set. The results of [15] introduced the concepts of Sequence Based Estimation (SBE) for the Binomial distribution. This current paper generalizes these results for the multinomial “two-at-a-time” scenario. We invoke a novel phenomenon called “Occlusion” that can be described as follows: By “concealing” certain observations, we map the estimation problem onto a lower-dimensional binomial space. Once these occluded SBEs have been computed, we demonstrate how the overall Multinomial SBE (MSBE) can be obtained by mapping several lower-dimensional estimates onto the original higher-dimensional space. We formally prove and experimentally demonstrate the convergence of the corresponding estimates.

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Keywords Estimation of multinomials, Estimation using sequential information, Fused estimation methods, Sequence based estimation, Sequential information
Persistent URL
Series Lecture Notes in Computer Science
Oommen, J, & Kim, S.-W. (Sang-Woon). (2016). On the foundations of multinomial Sequence based estimation. In Lecture Notes in Computer Science. doi:10.1007/978-3-319-45243-2_20