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A line of recent work has analyzed the behavior of the Expectation-Maximization (EM) algorithm in the well-specified setting, in which the population likelihood is locally strongly concave around its maximizing argument. Examples include…

Expectation Propagation is a very popular algorithm for variational inference, but comes with few theoretical guarantees. In this article, we prove that the approximation errors made by EP can be bounded. Our bounds have an asymptotic…

We study a parametric estimation problem related to moment condition models. As an alternative to the generalized empirical likelihood (GEL) and the generalized method of moments (GMM), a Bayesian approach to the problem can be adopted,…

We establish some new non-asymptotical lower bounds for deviation of regular unbiased estimation of unknown parameter from its true value in different norms, alike the classical Rao-Kramer's inequality. We show that if the new norm is…

Consider a setting with $N$ independent individuals, each with an unknown parameter, $p_i \in [0, 1]$ drawn from some unknown distribution $P^\star$. After observing the outcomes of $t$ independent Bernoulli trials, i.e., $X_i \sim…

Longitudinal imaging studies are essential to understanding the neural development of neuropsychiatric disorders, substance use disorders, and the normal brain. The main objective of this paper is to develop a two-stage adjusted…

We investigate the convergence properties of the EM algorithm when applied to overspecified Gaussian mixture models -- that is, when the number of components in the fitted model exceeds that of the true underlying distribution. Focusing on…

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…

The bias of an estimator is defined as the difference of its expected value from the parameter to be estimated, where the expectation is with respect to the model. Loosely speaking, small bias reflects the desire that if an experiment is…

The Expectation-Maximization (EM) algorithm is an iterative method to maximize the log-likelihood function for parameter estimation. Previous works on the convergence analysis of the EM algorithm have established results on the asymptotic…

In the usual statistical inference problem, we estimate an unknown parameter of a statistical model using the information in the random sample. A priori information about the parameter is also known in several real-life situations. One such…

The Expectation Maximization (EM) algorithm is of key importance for inference in latent variable models including mixture of regressors and experts, missing observations. This paper introduces a novel EM algorithm, called…

Estimation and inference for the Average Treatment Effect (ATE) is a cornerstone of causal inference and often serves as the foundation for developing procedures for more complicated settings. Although traditionally analyzed in a batch…

Although persistent excitation is often acknowledged as a sufficient condition to exponentially converge in the field of adaptive parameter estimation, it must be noted that in practical applications this may be unguaranteed. Recently, more…

Causal inference problems often involve continuous treatments, such as dose, duration, or frequency. However, identifying and estimating standard dose-response estimands requires that everyone has some chance of receiving any level of the…

We revisit the recently introduced Local Glivenko-Cantelli setting, which studies distribution-dependent uniform convergence rates of the Empirical Mean Estimator (EME). In this work, we investigate generalizations of this setting where…

For the estimation of cumulative link models for ordinal data, the bias-reducing adjusted score equations in \citet{firth:93} are obtained, whose solution ensures an estimator with smaller asymptotic bias than the maximum likelihood…

This paper studies the identification, estimation, and hypothesis testing problem in complete and incomplete economic models with testable assumptions. Testable assumptions ($A$) give strong and interpretable empirical content to the models…

Much of the theory of estimation for exponential family models, which include exponential-family random graph models (ERGMs) as a special case, is well-established and maximum likelihood estimates in particular enjoy many desirable…

In many applications, parameters of interest are estimated by solving some non-smooth estimating equations with $U$-statistic structure. Jackknife empirical likelihood (JEL) approach can solve this problem efficiently by reducing the…