Related papers: Maximum Likelihood under constraints: Degeneracies…
We study an optimal control problem in which both the objective function and the dynamic constraint contain an uncertain parameter. Since the distribution of this uncertain parameter is not exactly known, the objective function is taken as…
We extend the constrained maximum likelihood estimation theory for parameters of a completely identified model, proposed by Aitchison and Silvey (1958), to parameters arising from a partially identified model. With a partially identified…
Statistical modeling of multivariate and spatial extreme events has attracted broad attention in various areas of science. Max-stable distributions and processes are the natural class of models for this purpose, and many parametric families…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
In this paper, we study the maximum likelihood estimate of the probability mass function (pmf) of $n$ independent and identically distributed (i.i.d.) random variables, in the non-asymptotic regime. We are interested in characterizing the…
In the statistical problem of denoising, Bayes and empirical Bayes methods can "overshrink" their output relative to the latent variables of interest. This work is focused on constrained denoising problems which mitigate such phenomena. At…
We introduce estimation and test procedures through divergence minimization for models satisfying linear constraints with unknown parameter. Several statistical examples and motivations are given. These procedures extend the empirical…
Missing covariates are not uncommon in capture-recapture studies. When covariate information is missing at random in capture-recapture data, an empirical full likelihood method has been demonstrated to outperform…
The likelihood ratio statistic, with its asymptotic $\chi^2$ distribution at regular model points, is often used for hypothesis testing. At model singularities and boundaries, however, the asymptotic distribution may not be $\chi^2$, as…
In this work, we study non-parametric hypothesis testing problem with distribution function constraints. The empirical likelihood ratio test has been widely used in testing problems with moment (in)equality constraints. However, some…
We consider tests of hypotheses when the parameters are not identifiable under the null in semiparametric models, where regularity conditions for profile likelihood theory fail. Exponential average tests based on integrated profile…
Estimations of physical parameters using data usually involve non-uniform experimental efficiencies. In this article, a method of maximum likelihood fit is introduced using the efficiency as a weight, while the probability distribution…
We consider the problem of estimating the population probability distribution given a finite set of multivariate samples, using the maximum entropy approach. In strict keeping with Jaynes' original definition, our precise formulation of the…
We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed…
The problem of astrometry is revisited from the perspective of analyzing the attainability of well-known performance limits (the Cramer-Rao bound) for the estimation of the relative position of light-emitting (usually point-like) sources on…
A solution to control for nonresponse bias consists of multiplying the design weights of respondents by the inverse of estimated response probabilities to compensate for the nonrespondents. Maximum likelihood and calibration are two…
Empirical likelihood is a popular nonparametric or semi-parametric statistical method with many nice statistical properties. Yet when the sample size is small, or the dimension of the accompanying estimating function is high, the…
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…
High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random-walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive: the…
The likelihood function plays a pivotal role in statistical inference; it is adaptable to a wide range of models and the resultant estimators are known to have good properties. However, these results hinge on correct specification of the…