Related papers: Maximum likelihood estimation in hidden Markov mod…
Linear birth-and-death processes (LBDPs) are foundational stochastic models in population dynamics, evolutionary biology, and hematopoiesis. Estimating parameters from discretely observed data is computationally demanding due to irregular…
Skew normal mixture models provide a more flexible framework than the popular normal mixtures for modelling heterogeneous data with asymmetric behaviors. Due to the unboundedness of likelihood function and the divergency of shape…
We present a review of some recent results on estimation of location parameter for several models of observations with cusp-type singularity at the change point. We suppose that the cusp-type models fit better to the real phenomena…
The purpose of this paper is to study the convergence of the quasi-maximum likelihood (QML) estimator for long memory linear processes. We first establish a correspondence between the long-memory linear process representation and the…
Hawkes Processes have undergone increasing popularity as default tools for modeling self- and mutually exciting interactions of discrete events in continuous-time event streams. A Maximum Likelihood Estimation (MLE) unconstrained…
The Hidden Markov Model (HMM) is one of the mainstays of statistical modeling of discrete time series, with applications including speech recognition, computational biology, computer vision and econometrics. Estimating an HMM from its…
We consider finite state space stationary hidden Markov models (HMMs) in the situation where the number of hidden states is unknown. We provide a frequentist asymptotic evaluation of Bayesian analysis methods. Our main result gives…
We consider together the retrospective and the sequential change-point detection in a general class of integer-valued time series. The conditional mean of the process depends on a parameter $\theta^*$ which may change over time. We propose…
We study the maximum likelihood estimation (MLE) in the multivariate deviated model where the data are generated from the density function $(1-\lambda^{\ast})h_{0}(x)+\lambda^{\ast}f(x|\mu^{\ast}, \Sigma^{\ast})$ in which $h_{0}$ is a known…
State-space models have been used in many applications, including econometrics, engineering, medical research, etc. The maximum likelihood estimation (MLE) of the static parameter of general state-space models is not straightforward because…
Rue and Held (2005) proposed a method for efficiently computing the Gaussian likelihood for stationary Markov random field models, when the data locations fall on a complete regular grid, and the model has no additive error term. The…
The transition density of a diffusion process does not admit an explicit expression in general, which prevents the full maximum likelihood estimation (MLE) based on discretely observed sample paths. A\"{\i}t-Sahalia [J. Finance 54 (1999)…
Multi-state models are frequently applied for representing processes evolving through a discrete set of state. Important classes of multi-state models arise when transitions between states may depend on the time since entry into the current…
In this work, we investigate Gaussian Mixture Models ({\it abbrv} GMM) and the related problem of non parametric maximum likelihood estimation ({\it abbrv} NPMLE) from the perspective of statistical mechanics. In particular, we establish…
This paper establishes the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator (QMLE) for a GARCH process with periodically time-varying parameters. We first give a necessary and sufficient condition for…
With the rapid advancements in technology for data collection, the application of the spatial autoregressive (SAR) model has become increasingly prevalent in real-world analysis, particularly when dealing with large datasets. However, the…
Many quantum algorithms contain an important subroutine, the quantum amplitude estimation. As the name implies, this is essentially the parameter estimation problem and thus can be handled via the established statistical estimation theory.…
We consider the problem of selecting covariates in spatial linear models with Gaussian process errors. Penalized maximum likelihood estimation (PMLE) that enables simultaneous variable selection and parameter estimation is developed and,…
Hidden Markov Models (HMMs) can be accurately approximated using co-occurrence frequencies of pairs and triples of observations by using a fast spectral method in contrast to the usual slow methods like EM or Gibbs sampling. We provide a…
In various practical situations, we encounter data from stochastic processes which can be efficiently modelled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, the most common estimation and inference…