Search Constraints

Start Over
Filtering by: Creator Kim, Sang-Woon Remove constraint Creator: Kim, Sang-Woon

Search Results

  • On the foundations of multinomial Sequence based estimation

    Resource Type:
    Conference Proceeding
    Creator:
    Oommen, B. John and Kim, Sang-Woon
    Abstract:
    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.
    Date Created:
    2016-01-01

  • Multinomial sequence based estimation using contiguous subsequences of length three

    Resource Type:
    Conference Proceeding
    Creator:
    Kim, Sang-Woon and Oommen, B. John
    Abstract:
    The Maximum Likelihood (ML) and Bayesian estimation paradigms work within the model that the data, from which the parameters are to be estimated, is treated as a set rather than as a sequence. The pioneering paper that dealt with the field of sequence-based estimation [2] involved utilizing both the information in the observations and in their sequence of appearance. The results of [2] introduced the concepts of Sequence Based Estimation (SBE) for the Binomial distribution, where the authors derived the corresponding MLE results when the samples are taken two-at-a-time, and then extended these for the cases when they are processed three-at-a-time, four-at-a-time etc. These results were generalized for the multinomial “two-at-a-time” scenario in [3]. This paper (This paper is dedicated to the memory of Dr. Mohamed Kamel, who was a close friend of the first author.) now further generalizes the results found in [3] for the multinomial case and for subsequences of length 3. The strategy used in [3] (and also here) involves a novel phenomenon called “Occlusion” that has not been reported in the field of estimation. The phenomenon can be described as follows: By occluding (hiding or concealing) certain observations, we map the estimation problem onto a lower-dimensional space, i.e., onto a binomial space. Once these occluded SBEs have been computed, the overall Multinomial SBE (MSBE) can be obtained by combining these lower-dimensional estimates. In each case, we formally prove and experimentally demonstrate the convergence of the corresponding estimates.
    Date Created:
    2016-01-01