Related papers: Estimating the Missing Mass, Partition Function or…
Estimating the underlying distribution from \textit{iid} samples is a classical and important problem in statistics. When the alphabet size is large compared to number of samples, a portion of the distribution is highly likely to be…
Big data is ubiquitous in practices, and it has also led to heavy computation burden. To reduce the calculation cost and ensure the effectiveness of parameter estimators, an optimal subset sampling method is proposed to estimate the…
The Curie-Weiss model, originally used to study phase transitions in statistical mechanics, has been adapted to model phenomena in social sciences where many agents interact with each other. Reconstructing the probability measure of a…
The estimation of coverage probabilities, and in particular of the missing mass, is a classical statistical problem with applications in numerous scientific fields. In this paper, we study this problem in relation to randomized data…
In probability theory, the partition function is a factor used to reduce any probability function to a density function with total probability of one. Among other statistical models used to represent joint distribution, Markov random fields…
In this paper, different strands of literature are combined in order to obtain algorithms for semi-parametric estimation of discrete choice models that include the modelling of unobserved heterogeneity by using mixing distributions for the…
There exist some testing procedures based on the maximum mean discrepancy (MMD) to address the challenge of model specification. However, they ignore the presence of estimated parameters in the case of composite null hypotheses. In this…
We consider two nonparametric procedures for estimating a concave distribution function based on data corrupted with additive noise generated by a bounded decreasing density on $(0,\infty)$. For the maximum likelihood (ML) estimator and…
Given $iid$ observations from an unknown absolute continuous distribution defined on some domain $\Omega$, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function.…
A central problem in computational statistics is to convert a procedure for sampling combinatorial from an objects into a procedure for counting those objects, and vice versa. Weconsider sampling problems coming from *Gibbs distributions*,…
Theoretical guarantees are established for a standard estimator in a semi-parametric finite mixture model, where each component density is modeled as a product of univariate densities under a conditional independence assumption. The focus…
In this paper, we develop an approach for the exact determination of the minimum sample size for estimating the parameter of an integer-valued random variable, which is parameterized by its expectation. Under some continuity and unimodal…
We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $ M…
Suppose we observe a trajectory of length $n$ from an exponentially $\alpha$-mixing stochastic process over a finite but potentially large state space. We consider the problem of estimating the probability mass placed by the stationary…
We present an approach to deep estimation of discrete conditional probability distributions. Such models have several applications, including generative modeling of audio, image, and video data. Our approach combines two main techniques:…
Bayesian estimation is increasingly popular for performing model based inference to support policymaking. These data are often collected from surveys under informative sampling designs where subject inclusion probabilities are designed to…
Our primary aim is to find an estimate of the expected shortfall in various situations: (1) Nonparametric situation, when the probability distribution of the incurred loss is unknown, only satisfying some general conditions. Then, following…
Mixture models are regularly used in density estimation applications, but the problem of estimating the mixing distribution remains a challenge. Nonparametric maximum likelihood produce estimates of the mixing distribution that are…
Given a sequence of observations from a discrete-time, finite-state hidden Markov model, we would like to estimate the sampling distribution of a statistic. The bootstrap method is employed to approximate the confidence regions of a…
We propose a new approach for estimating the parameters of a probability distribution. It consists on combining two new methods of estimation. The first is based on the definition of a new distance measuring the difference between…