Related papers: Local Estimation of a Multivariate Density and its…
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 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…
A novel computational approach to log-concave density estimation is proposed. Previous approaches utilize the piecewise-affine parametrization of the density induced by the given sample set. The number of parameters as well as non-smooth…
One key issue in several astrophysical problems is the evaluation of the density probability function underlying an observational discrete data set. We here review two non-parametric density estimators which recently appeared in the…
We derive a formula to calculate the local change to the log of any density of states for smooth real observables. Using this in Monte-Carlo simulations, we are able to calculate the expectation value of the observable with a precision…
We present a local density estimator based on first order statistics. To estimate the density at a point, $x$, the original sample is divided into subsets and the average minimum sample distance to $x$ over all such subsets is used to…
In a previous article, a least square regression estimation procedure was proposed: first, we condiser a family of functions and study the properties of an estimator in every unidimensionnal model defined by one of these functions; we then…
Multivariate density estimation is a popular technique in statistics with wide applications including regression models allowing for heteroskedasticity in conditional variances. The estimation problems become more challenging when…
We study the problem of computing the maximum likelihood estimator (MLE) of multivariate log-concave densities. Our main result is the first computationally efficient algorithm for this problem. In more detail, we give an algorithm that, on…
Accurate density estimation methodologies play an integral role in a variety of scientific disciplines, with applications including simulation models, decision support tools, and exploratory data analysis. In the past, histograms and kernel…
In recent years, log-concave density estimation via maximum likelihood estimation has emerged as a fascinating alternative to traditional nonparametric smoothing techniques, such as kernel density estimation, which require the choice of one…
This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample…
We consider a continuous-time stochastic volatility model. The model contains a stationary volatility process, the multivariate density of the finite dimensional distributions of which we aim to estimate. We assume that we observe the…
Let X_1, ..., X_n be independent and identically distributed random vectors with a log-concave (Lebesgue) density f. We first prove that, with probability one, there exists a unique maximum likelihood estimator of f. The use of this…
In this paper we study the problem of pointwise density estimation from observations with multiplicative measurement errors. We elucidate the main feature of this problem: the influence of the estimation point on the estimation accuracy. In…
We study the problem of bivariate discrete or continuous probability density estimation under low-rank constraints.For discrete distributions, we assume that the two-dimensional array to estimate is a low-rank probability matrix. In the…
This article examines density estimation by combining a parametric approach with a nonparametric factor. The plug-in parametric estimator is seen as a crude estimator of the true density and is adjusted by a nonparametric factor. The…
We present theoretical properties of the log-concave maximum likelihood estimator of a density based on an independent and identically distributed sample in $\mathbb{R}^d$. Our study covers both the case where the true underlying density is…
Non-parametric estimation of a multivariate density estimation is tackled via a method which combines traditional local smoothing with a form of global smoothing but without imposing a rigid structure. Simulation work delivers encouraging…
We consider two kinds of stochastic volatility models. Both kinds of models contain a stationary volatility process, the density of which, at a fixed instant in time, we aim to estimate. We discuss discrete time models where for instance a…