Lower Bound of Variance for Multipartite Structure of Hidden Markov Model
Gohar Ayub · Indian Journal of Science and Technology · 2018
Objective: This study derives an expression for obtaining lower bound of variance for estimates of hidden Markov model. Also, this study provides a parametric procedure for lower bound of variance. Methods/Statistical Analysis: In study a multipartite form of hidden Markov model considered. The states of model observed at time “2t-1” and “2t” respectively. The lower bound expression obtained by Louis methodology. The secondary data is used to study the validity of proposed lower bound. This dataset is a time series and named as “tree ring width”. Study also defines a parametric procedure for computing lower bound of variance. Findings: The study obtained the lower bound of variance for the maximum likelihood estimates of model using real-world data. The study compares the results of variance obtained by two procedures for various combinations of the states. It is found that for some combination of states, the lower bound of variance by two approaches found almost same. While for many combinations of states the lower bound of variance from proposed procedure found smaller than parametric procedure. The overall comparison lower bound of variance for maximum likelihood by proposed method explaining less variation in dataset then conventional i.e. parametric procedure. Conclusion: The study concluded that results for variance by derived expression found sharpen than those of parametric procedure. Keywords: Hidden Markov Model, Lower Bound Variance, Maximum Likelihood, Multipartite Structure, Parametric Procedure