Related papers: Maximum likelihood estimation of a log-concave den…

In reliability and life testing studies, the topic of estimating hazard rate has received great attention in recent years since an estimate of hazard rate is a quite useful tool for making decisions. Some works have included nonparametric…

If the log likelihood is approximately quadratic with constant Hessian, then the maximum likelihood estimator (MLE) is approximately normally distributed. No other assumptions are required. We do not need independent and identically…

In algebraic statistics, the maximum likelihood degree of a statistical model is the number of complex critical points of its log-likelihood function. A priori knowledge of this number is useful for applying techniques of numerical…

Asymptotic properties of three estimators of probability density function of sample maximum $f_{(m)}:=mfF^{m-1}$ are derived, where $m$ is a function of sample size $n$. One of the estimators is the parametrically fitted by the…

In this article, we revisit the problem of estimating the unknown zero-symmetric distribution in a two-component location mixture model, considered in previous works, now under the assumption that the zero-symmetric distribution has a…

Linear structural equation models postulate noisy linear relationships between variables of interest. Each model corresponds to a path diagram, which is a mixed graph with directed edges that encode the domains of the linear functions and…

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…

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…

We consider the problem of estimating the distribution function, the density and the hazard rate of the (unobservable) event time in the current status model. A well studied and natural nonparametric estimator for the distribution function…

This paper focuses on nonparametric statistical inference of the hazard rate function of discrete distributions based on $\delta$-record data. We derive the explicit expression of the maximum likelihood estimator and determine its exact…

This Note presents original rates of convergence for the deconvolution problem. We assume that both the estimated density and noise density are supersmooth and we compute the risk for two kinds of estimators.

In this article, we revisit the problem of fitting a mixture model under the assumption that the mixture components are symmetric and log-concave. To this end, we first study the nonparametric maximum likelihood estimation (NPMLE) of a…

This paper considers the asymptotic properties of the recursive maximum likelihood estimation in hidden Markov models. The paper is focused on the asymptotic behavior of the log-likelihood function and on the point-convergence and…

We estimate the density and its derivatives using a local polynomial approximation to the logarithm of an unknown density $f$. The estimator is guaranteed to be nonnegative and achieves the same optimal rate of convergence in the interior…

We provide estimates of the rate of strong approximation and bounds for probabilities of moderate deviations in the CLT for the $L_1$-norm of the kernel density estimator without any assumptions on the density and assuming that the kernel…

This paper considers the nonparametric maximum likelihood estimator (MLE) for the joint distribution function of an interval censored survival time and a continuous mark variable. We provide a new explicit formula for the MLE in this…

Jakimiuk et al. (2024) have proved that, if $X$ is an ultra log-concave random variable with integral mean, then $$\max_n \mathbb{P}\{X=n\} \geq \max_n \mathbb{P} \{Z=n\}\,,$$ where $Z$ is a Poisson random variable with the parameter…

The paper deals with the problem of nonparametric estimating the $L_p$--norm, $p\in (1,\infty)$, of a probability density on $R^d$, $d\geq 1$ from independent observations. The unknown density %to be estimated is assumed to belong to a ball…

In this paper, we study the problem of sampling from a given probability density function that is known to be smooth and strongly log-concave. We analyze several methods of approximate sampling based on discretizations of the (highly…

Logconcave functions represent the current frontier of efficient algorithms for sampling, optimization and integration in R^n. Efficient sampling algorithms to sample according to a probability density (to which the other two problems can…