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An expanded family of mixtures of multivariate power exponential distributions is introduced. While fitting heavy-tails and skewness has received much attention in the model-based clustering literature recently, we investigate the use of a…
Maximum Likelihood Estimation (MLE) and Likelihood Ratio Test (LRT) are widely used methods for estimating the transition probability matrix in Markov chains and identifying significant relationships between transitions, such as equality.…
Debiased machine learning estimators for smooth functionals in nonparametric models can exhibit substantial variability and instability, often leading practitioners to instead rely on parametric or semiparametric working models. Such…
Targeted maximum likelihood estimation is a general methodology combining flexible ensemble learning and semiparametric efficiency theory in a two-step procedure for estimation of causal parameters. Proposed targeted maximum likelihood…
This paper derives the nonparametric maximum likelihood estimator (NPMLE) of a distribution function from observations which are subject to both bias and censoring. The NPMLE is obtained by a simple EM algorithm which is an extension of the…
Growing-dimensional data with likelihood unavailable are often encountered in various fields. This paper presents a penalized exponentially tilted likelihood (PETL) for variable selection and parameter estimation for growing dimensional…
The Laplace approximation (LA) has been proposed as a method for approximating the marginal likelihood of statistical models with latent variables. However, the approximate maximum likelihood estimators (MLEs) based on the LA are often…
The exponential-family random graph models (ERGMs) have emerged as an important framework for modeling social networks for a wide variety of relational types. ERGMs for valued networks are less well-developed than their unvalued…
We prove the asymptotic properties of the maximum likelihood estimator (MLE) in time-varying transition probability (TVTP) regime-switching models. This class of models extends the constant regime transition probability in Markov-switching…
Standard maximum likelihood estimation cannot be applied to discrete energy-based models in the general case because the computation of exact model probabilities is intractable. Recent research has seen the proposal of several new…
Given a heterogeneous time-series sample, the objective is to find points in time (called change points) where the probability distribution generating the data has changed. The data are assumed to have been generated by arbitrary unknown…
Many modern products exhibit high reliability, often resulting in long times to failure. Consequently, conducting experiments under normal operating conditions may require an impractically long duration to obtain sufficient failure data for…
This paper addresses maximum likelihood (ML) estimation based model fitting in the context of extrasolar planet detection. This problem is featured by the following properties: 1) the candidate models under consideration are highly…
An exponentially weighted moving model (EWMM) for a vector time series fits a new data model each time period, based on an exponentially fading loss function on past observed data. The well known and widely used exponentially weighted…
The parametric estimators applied by rolling are commonly used in the analysis of time series with nonlinear features, such as structural change due to time varying parameters and local trends. This paper examines the properties of rolling…
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…
Expectation maximization (EM) is the default algorithm for fitting probabilistic models with missing or latent variables, yet we lack a full understanding of its non-asymptotic convergence properties. Previous works show results along the…
This paper considers a distributed stochastic optimization problem where the goal is to minimize the time average of a cost function subject to a set of constraints on the time averages of a related stochastic processes called penalties. We…
We consider the problem of estimating the parameters of a non-stationary Hawkes process with time-dependent reproduction rate and baseline intensity. Our approach relies on the standard maximum likelihood estimator (MLE), coinciding with…
A novel first-order moving-average model for analyzing time series observed at irregularly spaced intervals is introduced. Two definitions are presented, which are equivalent under Gaussianity. The first one relies on normally distributed…