Related papers: Maximum likelihood estimator and its consistency f…
The stationary distribution of allele frequencies under a variety of Wright--Fisher $k$-allele models with selection and parent independent mutation is well studied. However, the statistical properties of maximum likelihood estimates of…
The Maximum Likelihood Estimator (MLE) serves an important role in statistics and machine learning. In this article, for i.i.d. variables, we obtain constant-specified and sharp concentration inequalities and oracle inequalities for the MLE…
We find limiting distributions of the nonparametric maximum likelihood estimator (MLE) of a log-concave density, that is, a density of the form $f_0=\exp\varphi_0$ where $\varphi_0$ is a concave function on $\mathbb{R}$. The pointwise…
Maximum regularized likelihood estimators (MRLEs) are arguably the most established class of estimators in high-dimensional statistics. In this paper, we derive guarantees for MRLEs in Kullback-Leibler divergence, a general measure of…
This paper investigates the asymptotic distribution of the maximum-likelihood estimate (MLE) in multinomial logistic models in the high-dimensional regime where dimension and sample size are of the same order. While classical large-sample…
Max-stable distributions and processes are important models for extreme events and the assessment of tail risks. The full, multivariate likelihood of a parametric max-stable distribution is complicated and only recent advances enable its…
Suppose that $\m{U} = (U_1, \ldots , U_d) $ has a Uniform$([0,1]^d)$ distribution, that $\m{Y} = (Y_1 , \ldots , Y_d) $ has the distribution $G$ on $\RR_+^d$, and let $\m{X} = (X_1 , \ldots , X_d) = (U_1 Y_1 , \ldots , U_d Y_d )$. The…
The paper studies large sample asymptotic properties of the Maximum Likelihood Estimator (MLE) for the parameter of a continuous time Markov chain, observed in white noise. Using the method of weak convergence of likelihoods due to…
We prove the strong consistency and the asymptotic normality of the maximum likelihood estimator of the parameters of a general conditionally heteroscedastic model with $\alpha$-stable innovations. Then, we relax the assumptions and only…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
The advent of data science has spurred interest in estimating properties of distributions over large alphabets. Fundamental symmetric properties such as support size, support coverage, entropy, and proximity to uniformity, received most…
This paper introduces a Monte Carlo method for maximum likelihood inference in the context of discretely observed diffusion processes. The method gives unbiased and a.s.\@ continuous estimators of the likelihood function for a family of…
We consider the homogeneous stochastic differential equation with unknown parameter to be estimated. We prove that the standard maximum likelihood estimate is strongly consistent under very mild conditions. There are also established the…
We consider a random walker in a dynamic random environment given by a system of independent simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on…
We consider parameter estimation in finite hidden state space Markov models with time-dependent inhomogeneous noise, where the inhomogeneity vanishes sufficiently fast. Based on the concept of asymptotic mean stationary processes we prove…
We consider one infinite path of a Random Walk in Random Environment (RWRE, for short) in an unknown environment. This environment consists of either i.i.d.\ site or bond randomness. At each position the random walker stops and tells us the…
We consider the problem of localization of Poisson source by the observations of inhomogeneous Poisson processes. We suppose that there are $k$ detectors on the plane and each detector provides the observations of Poisson processes whose…
Maximum likelihood estimation (MLE) is a fundamental problem in statistics. Characteristics of the MLE problem for discrete algebraic statistical models are reflected in the geometry of the $\textit{likelihood correspondence}$, a variety…
We propose and study properties of maximum likelihood estimators in the class of conditional transformation models. Based on a suitable explicit parameterisation of the unconditional or conditional transformation function, we establish a…
We study maximum likelihood estimation in Gaussian graphical models from a geometric point of view. An algebraic elimination criterion allows us to find exact lower bounds on the number of observations needed to ensure that the maximum…