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Motivated by studying asymptotic properties of the maximum likelihood estimator (MLE) in stochastic volatility (SV) models, in this paper we investigate likelihood estimation in state space models. We first prove, under some regularity…
Maximum likelihood is the most widely used statistical estimation technique. Recent work by the authors introduced a general methodology for the construction of estimators for functionals in parametric models, and demonstrated improvements…
Determinantal point processes (DPPs) have wide-ranging applications in machine learning, where they are used to enforce the notion of diversity in subset selection problems. Many estimators have been proposed, but surprisingly the basic…
This paper considers maximum likelihood (ML) estimation in a large class of models with hidden Markov regimes. We investigate consistency of the ML estimator and local asymptotic normality for the models under general conditions which allow…
Maximum likelihood estimation in statistics leads to the problem of maximizing a product of powers of polynomials. We study the algebraic degree of the critical equations of this optimization problem. This degree is related to the number of…
In this paper, we obtain new results on the weak and strong consistency of the maximum and integrated conditional likelihood estimators for the community detection problem in the Stochastic Block Model with $k$ communities and unknown…
This paper investigates maximum likelihood estimation for direct system identification in networks of dynamical systems. We establish that the proposed approach is both consistent and efficient. In addition, it is more generally applicable…
Targeted maximum likelihood estimation (TMLE) is a general method for estimating parameters in semiparametric and nonparametric models. Each iteration of TMLE involves fitting a parametric submodel that targets the parameter of interest. We…
In this paper, we develop asymptotic theories for a class of latent variable models for large-scale multi-relational networks. In particular, we establish consistency results and asymptotic error bounds for the (penalized) maximum…
This paper defines a Maximum Likelihood Estimator (MLE) for the admittance matrix estimation of distribution grids, utilising voltage magnitude and power measurements collected only from common, unsychronised measuring devices (Smart…
We present new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. Our theory builds on the idea of using subsets of the full data to establish consistency of estimators based on the full…
This paper develops several interesting, significant, and interconnected approaches to nonparametric or semi-parametric statistical inferences. The overwhelmingly favoured maximum likelihood estimator (MLE) under parametric model is…
Introduced by Kiefer and Wolfowitz \cite{KW56}, the nonparametric maximum likelihood estimator (NPMLE) is a widely used methodology for learning mixture odels and empirical Bayes estimation. Sidestepping the non-convexity in mixture…
We study multivariate Gaussian models that are described by linear conditions on the concentration matrix. We compute the maximum likelihood (ML) degrees of these models. That is, we count the critical points of the likelihood function over…
Most statistical software packages implement numerical strategies for computation of maximum likelihood estimates in random effects models. Little is known, however, about the algebraic complexity of this problem. For the one-way layout…
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…
The {\lambda}-exponential family has recently been proposed to generalize the exponential family. While the exponential family is well-understood and widely used, this it not the case of the {\lambda}-exponential family. However, many…
We consider the parameter estimation problem of a probabilistic generative model prescribed using a natural exponential family of distributions. For this problem, the typical maximum likelihood estimator usually overfits under limited…
The maximum likelihood threshold (MLT) of a graph $G$ is the minimum number of samples to almost surely guarantee existence of the maximum likelihood estimate in the corresponding Gaussian graphical model. We give a new characterization of…
This paper develops a new family of estimators, the minimum density power divergence estimators (MDPDEs), for the parameters of the one-shot device model as well as a new family of test statistics, Z-type test statistics based on MDPDEs,…