Related papers: Maximum likelihood estimator and its consistency f…
The pattern maximum likelihood (PML) estimate, introduced by Orlitsky et al., is an estimate of the multiset of probabilities in an unknown probability distribution $\mathbf{p}$, the estimate being obtained from $n$ i.i.d. samples drawn…
This paper deals with the problem of inference associated with linear fractional diffusion process with random effects in the drift. In particular we are concerned with the maximum likelihood estimators (MLE) of the random effect…
We study the problem of maximum likelihood estimation given one data sample ($n=1$) over Brownian Motion Tree Models (BMTMs), a class of Gaussian models on trees. BMTMs are often used as a null model in phylogenetics, where the one-sample…
For many diseases, logistic and other constraints often render large incidence studies difficult, if not impossible, to carry out. This becomes a drawback, particularly when a new incidence study is needed each time the disease incidence…
The behavior of the maximal displacement of a supercritical branching random walk has been a subject of intense studies for a long time. But only recently the case of time-inhomogeneous branching has gained focus. The contribution of this…
This paper develops a unified estimation framework, the Maximum Ideal Likelihood Estimation (MILE), for general parametric models with latent variables. Unlike traditional approaches relying on the marginal likelihood of the observed data,…
We suggest an iterative approach to computing K-step maximum likelihood estimates (MLE) of the parametric components in semiparametric models based on their profile likelihoods. The higher order convergence rate of K-step MLE mainly depends…
We show that the maximum likelihood estimator (MLE) is an effective tool for mitigating non-flow effects in flow analysis. To this end, one constructs two toy models that simulate non-flow contributions corresponding to particle decay and…
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)…
The main approach to inference for multivariate extremes consists in approximating the joint upper tail of the observations by a parametric family arising in the limit for extreme events. The latter may be expressed in terms of…
Maximum likelihood estimators are used extensively to estimate unknown parameters of stochastic trait evolution models on phylogenetic trees. Although the MLE has been proven to converge to the true value in the independent-sample case, we…
The consistency of the maximum likelihood estimator for mixtures of elliptically-symmetric distributions for estimating its population version is shown, where the underlying distribution $P$ is nonparametric and does not necessarily belong…
Over the last decades, the family of $\alpha$-stale distributions has proven to be useful for modelling in telecommunication systems. Particularly, in the case of radar applications, finding a fast and accurate estimation for the amplitude…
The stochastic motions of a diffusing particle contain information concerning the particle's interactions with binding partners and with its local environment. However, accurate determination of the underlying diffusive properties, beyond…
This paper rigorously establishes that the existence of the maximum likelihood estimate (MLE) in high-dimensional logistic regression models with Gaussian covariates undergoes a sharp `phase transition'. We introduce an explicit boundary…
We give answer to an open problem regarding consistency of the maximum likelihood estimators (MLEs) in generalized linear mixed models (GLMMs) involving crossed random effects. The solution to the open problem introduces an interesting,…
For the tree topology, previous studies show the maximum likelihood estimate (MLE) of a link/path takes a polynomial form with a degree that is one less than the number of descendants connected to the link/path. Since then, the main concern…
Markov regime switching models have been widely used in numerous empirical applications in economics and finance. However, the asymptotic distribution of the maximum likelihood estimator (MLE) has not been proven for some empirically…
Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…
We study statistical inference for small-noise-perturbed multiscale dynamical systems. We prove consistency, asymptotic normality, and convergence of all scaled moments of an appropriately-constructed maximum likelihood estimator (MLE) for…