Related papers: MLE for the parameters of bivariate interval-value…
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…
Several problems in statistics involve the combination of high-variance unbiased estimators with low-variance estimators that are only unbiased under strong assumptions. A notable example is the estimation of causal effects while combining…
As is the case for many curved exponential families, the computation of maximum likelihood estimates in a multivariate normal model with a Kronecker covariance structure is typically carried out with an iterative algorithm, specifically, a…
Variational approaches based on neural networks are showing promise for estimating mutual information (MI) between high dimensional variables. However, they can be difficult to use in practice due to poorly understood bias/variance…
We consider the problem of estimating the mean of a random vector based on i.i.d. observations and adversarial contamination. We introduce a multivariate extension of the trimmed-mean estimator and show its optimal performance under minimal…
We consider a one dimensional sub-ballistic random walk evolving in a parametric i.i.d. random environment. We study the asymptotic properties of the maximum likelihood estimator (MLE) of the parameter based on a single observation of the…
Maximum likelihood estimation (MLE) is a fundamental computational problem in statistics. The problem is to maximize the likelihood function with respect to given data on a statistical model. An algebraic approach to this problem is to…
In empirical research, when we have multiple estimators for the same parameter of interest, a central question arises: how do we combine unbiased but less precise estimators with biased but more precise ones to improve the inference? Under…
We consider the problem of estimating the covariance matrix of a random vector by observing i.i.d samples and each entry of the sampled vector is missed with probability $p$. Under the standard $L_4-L_2$ moment equivalence assumption, we…
This paper investigates the asymptotic properties of parameter estimation for the Ewens--Pitman partition with parameters $0<\alpha<1$ and $\theta>-\alpha$. Especially, we show that the maximum likelihood estimator (MLE) of $\alpha$ is…
We revisit the classical causal inference problem of estimating the average treatment effect in the presence of fully observed confounding variables using two-stage semiparametric methods. In existing theoretical studies of methods such as…
The density ratio model (DRM) provides a flexible and useful platform for combining information from multiple sources. In this paper, we consider statistical inference under two-sample DRMs with additional parameters defined through and/or…
We develop new methods to integrate experimental and observational data in causal inference. While randomized controlled trials offer strong internal validity, they are often costly and therefore limited in sample size. Observational data,…
This paper discusses regularized estimators in the multivariate statistical model as tools naturally arising within a Bayesian framework. First, a link is established between Bayesian estimation and inference under parameter rounding…
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 is an up-to-date introduction to and overview of the Minimum Description Length (MDL) Principle, a theory of inductive inference that can be applied to general problems in statistics, machine learning and pattern recognition. While MDL…
Objectives: Highly flexible nonparametric estimators have gained popularity in causal inference and epidemiology. Popular examples of such estimators include targeted maximum likelihood estimators (TMLE) and double machine learning (DML).…
The bivariate Gaussian distribution has been a key model for many developments in statistics. However, many real-world phenomena generate data that follow asymmetric distributions, and consequently bivariate normal model is inappropriate in…
The method of maximum likelihood estimation (MLE) is a widely used statistical approach for estimating the values of one or more unknown parameters of a probabilistic model based on observed data. In this tutorial, I briefly review the…
A Bayesian estimator aiming at improving the conditional MLE is proposed by introducing a pair of priors. After explaining the conditional MLE by the posterior mode under a prior, we define a promising estimator by the posterior mean under…