This article concerns the study of the asymptotic properties of the maximum likelihood estimator (MLE) for the general hidden semi-Markov model (HSMM) with backward recurrence time dependence. By transforming the general HSMM into a general hidden Markov model, we prove that under some regularity conditions, the MLE is strongly consistent and asymptotically normal. We also provide useful expres...

We investigate the rate of convergence of the distribution of the maximum likelihood estimator (MLE) of an unknown parameter in the drift coefficient of a stochastic process described by a linear stochastic differential equation driven by a fractional Brownian Motion (fBM). As a special case, we obtain the rate of convergence for the case of the fractional Ornstein-Uhlenbeck type process studie...

In this paper, we study the nonparametric maximum likelihood estimator (MLE) of a convex hazard function. We show that the MLE is consistent and converges at a local rate of n(2/5) at points x(0) where the true hazard function is positive and strictly convex. Moreover, we establish the pointwise asymptotic distribution theory of our estimator under these same assumptions. One notable feature of...

This article considers the nonparametric maximum likelihood estimator (MLE) for the joint distribution function of an interval censored survival time and a continuous mark variable. We derive a new explicit formula for the MLE that has both computational and theoretical advantages. Using this formula and the mark specific cumulative hazard function of Huang & Louis (1998), we derive the almost ...

In finite mixtures of location-scale distributions, if there is no constraint on the parameters then the maximum likelihood estimate does not exist. But when the ratios of the scale parameters are restricted appropriately, the maximum likelihood estimate exists. We prove that the maximum likelihood estimator (MLE) is strongly consistent, if the ratios of the scale parameters are restricted from...

We consider a particular maximum likelihood estimator (MLE) and a computationally-intensive Bayesian method for differentially private estimation of the linear mixed-effects model (LMM) with normal random errors. The LMM is important because it is used in small area estimation and detailed industry tabulations that present significant challenges for confidentiality protection of the underlying ...

Change point detecting problem is an important task in data mining applications. Standard statistical procedures for change point detection, based on maximum likelihood estimators, are complex and require building of parametric models of data. Instead, the methods of computational statistics replace complex statistical procedures with an amount of computation; so these methods become more popul...

This paper provides the Bayes estimators of the failure rate and reliability function for a one-parameter, exponential distribution by utilizing a point guess estimate of the parameter. For deriving the Bayes estimators, the prior distributions are chosen such that they are centered at the known prior values of parameters. The validity of proposed estimators is examined with respect to their ma...

An order-restricted (OR) statistical model can be expressed in the general form {Pθ | θ ∈ C}, where C is a convex cone in R. In general, no unbiased estimator exists for θ. In particular, the OR maximum likelihood estimator (ORMLE) is biased, although its aggregate mean square error is usually less than that of the unrestricted MLE (URMLE). Nonetheless, the bias and mean-square error (MSE) of a...