KeywordsHidden markov model Estimators Time series Algorithm States Sequence Probability.The Hidden Markov Model (HMM) is a powerful statistical tool for modeling generative sequences that can be characterized by an underlying process generating an observable sequence. Hidden Markov Model is one of the most basic and extensively used statistical tools for modeling the discrete time series. In this paper using transition probabilities and emission probabilities different algorithm are computed and modeled the series and the algorithms to solve the problems related to the hidden markov model are presented. Hidden markov models face some problems like learning about the model, evaluation process and estimate of parameters included in the model. The solution to these problems as forward-backward, Viterbi, and Baum Welch algorithm are discussed respectively and also useful for computation. A new hidden markov model is developed and estimates its parameters and also discussed the state space model.
In data analysis, count data modeling contributing a significant role. The Conway-Maxwell Poisson (COMP) is one of the flexible count data models to deal over and under dispersion. In the COMP regression model, when the explanatory variables are correlated, then the maximum likelihood estimator does not give efficient results due to the large standard error (SE) of the estimates. To overcome the effect of multicollinearity, we have proposed some ridge regression estimators in the COMP regression model by introducing dispersion parameter in the context of overdispersion, equidispersion, and underdispersion. The Iterative reweighted least method is used for the estimation of ridge regression coefficients in the COMP regression model. To evaluate the performance of the proposed estimators, we use mean squared error (MSE) as the performance evaluation criteria. Theoretical comparison of the proposed estimators with the competitor estimators is made and conditions of efficiency have been derived. The proposed estimator is evaluated with the help of a simulation study and two real applications. The results of the simulation study and real applications show the superiority of the proposed estimator because the proposed estimator produces smaller MSE and SEs of the COMP regression estimates with multicollinearity.
Poisson regression is a popular tool for modeling count data and is applied in medical sciences, engineering and others. Real data, however, are often over or underdispersed, and we cannot apply the Poisson regression. To overcome this issue, we consider a regression model based on the Conway–Maxwell Poisson (COMP) distribution. Generally, the maximum likelihood estimator is used for the estimation of unknown parameters of the COMP regression model. However, in the existence of multicollinearity, the estimates become unstable due to its high variance and standard error. To solve the issue, a new COMP Liu estimator is proposed for the COMP regression model with over-, equi-, and underdispersion. To assess the performance, we conduct a Monte Carlo simulation where mean squared error is considered as an evaluation criterion. Findings of simulation study show that the performance of our new estimator is considerably better as compared to others. Finally, an application is consider to assess the superiority of the proposed COMP Liu estimator. The simulation and application findings clearly demonstrated that the proposed estimator is superior to the maximum likelihood estimator.
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