Related papers: Consistent Density Estimation Under Discrete Mixtu…
Composite likelihood has shown promise in settings where the number of parameters $p$ is large due to its ability to break down complex models into simpler components, thus enabling inference even when the full likelihood is not tractable.…
This paper studies identifiability and convergence behaviors for parameters of multiple types in finite mixtures, and the effects of model fitting with extra mixing components. First, we present a general theory for strong identifiability,…
In recent years, multiple hypothesis testing has come to the forefront of statistical research, ostensibly in relation to applications in genomics and some other emerging fields. The false discovery rate (FDR) and its variants provide very…
Traditional density and quantile estimators are often inconsistent with each other. Their simultaneous usage may lead to inconsistent results. To address this issue, we propose a novel smooth density estimator that is naturally consistent…
This paper addresses the problem of full model estimation for non-parametric finite mixture models. It presents an approach for selecting the number of components and the subset of discriminative variables (i.e., the subset of variables…
We consider a multiplicative deconvolution problem, in which the density $f$ or the survival function $S^X$ of a strictly positive random variable $X$ is estimated nonparametrically based on an i.i.d. sample from a noisy observation $Y =…
Selectivity estimation aims at estimating the number of database objects that satisfy a selection criterion. Answering this problem accurately and efficiently is essential to many applications, such as density estimation, outlier detection,…
Density deconvolution deals with the estimation of the probability density function $f$ of a random signal from $n\geq1$ data observed with independent and known additive random noise. This is a classical problem in statistics, for which…
We study a non-parametric approach to multivariate density estimation. The estimators are piecewise constant density functions supported by binary partitions. The partition of the sample space is learned by maximizing the likelihood of the…
In a finite mixture of location-scale distributions maximum likelihood estimator does not exist because of the unboundedness of the likelihood function when the scale parameter of some mixture component approaches zero. In order to study…
Recent work has shown that models trained to the same objective, and which achieve similar measures of accuracy on consistent test data, may nonetheless behave very differently on individual predictions. This inconsistency is undesirable in…
Uncertainty estimation has been extensively studied in recent literature, which can usually be classified as aleatoric uncertainty and epistemic uncertainty. In current aleatoric uncertainty estimation frameworks, it is often neglected that…
Random discrete distributions, say $F,$ known as species sampling models, represent a rich class of models for classification and clustering, in Bayesian statistics and machine learning. They also arise in various areas of probability and…
Statistical inference for discrete time observations of an affine stochastic delay differential equation is considered. The main focus is on maximum pseudo-likelihood estimators, which are easy to calculate in practice. A more general class…
For high dimensional statistical models, researchers have begun to focus on situations which can be described as having relatively few moderately large coefficients. Such situations lead to some very subtle statistical problems. In…
We derive explicit a priori consistency error estimates for a standard finite element discretization of the Poisson equation on convex domains, where the domain is approximated by an internal convex polyhedron. The obtained explicit…
There has been significant study on the sample complexity of testing properties of distributions over large domains. For many properties, it is known that the sample complexity can be substantially smaller than the domain size. For example,…
The convergence and optimality of adaptive mixed finite element methods for the Poisson equation are established in this paper. The main difficulty for mixed finite element methods is the lack of minimization principle and thus the failure…
We study the nonparametric estimation of the jump density of a compound Poisson process from the discrete observation of one trajectory over $[0,T]$. We consider the microscopic regime when the sampling rate $\Delta=\Delta_T\rightarrow0$ as…
Empirical fixation densities, spatial distributions estimated from human eye-tracking data, are foundational to saliency benchmarking. They directly shape benchmark conclusions, leaderboard rankings, failure case analyses, and scientific…