Related papers: Attributing a probability to the shape of a probab…
This paper considers the problem of specifying a simple approximating density function for a given data set (x_1,...,x_n). Simplicity is measured by the number of modes but several different definitions of approximation are introduced. The…
The ratio between two probability density functions is an important component of various tasks, including selection bias correction, novelty detection and classification. Recently, several estimators of this ratio have been proposed. Most…
We propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing…
Density level sets are mainly estimated using one of three methodologies: plug-in, excess mass, or a hybrid approach. The plug-in methods are based on replacing the unknown density by some nonparametric estimator, usually the kernel. Thus,…
This paper introduces a practical sampling method for training surrogate models in the context of uncertainty propagation. We propose a heuristic method to uniformly draw samples within highest density regions of the density given by the…
Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…
Density level sets can be estimated using plug-in methods, excess mass algorithms or a hybrid of the two previous methodologies. The plug-in algorithms are based on replacing the unknown density by some nonparametric estimator, usually the…
One of the most commonly used methods for forming confidence intervals for statistical inference is the empirical bootstrap, which is especially expedient when the limiting distribution of the estimator is unknown. However, despite its…
We estimate on a compact interval densities with isolated irregularities, such as discontinuities or discontinuities in some derivatives. From independent and identically distributed observations we construct a kernel estimator with…
Variational inference is a general approach for approximating complex density functions, such as those arising in latent variable models, popular in machine learning. It has been applied to approximate the maximum likelihood estimator and…
A two-class mixture model, where the density of one of the components is known, is considered. We address the issue of the nonparametric adaptive estimation of the unknown probability density of the second component. We propose a randomly…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
We define a general method for finding a quasi-best approximant in sup-norm to a target density belonging to a given model, based on independent samples drawn from distributions which average to the target (which does not necessarily belong…
We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees…
Bump hunting deals with finding in sample spaces meaningful data subsets known as bumps. These have traditionally been conceived as modal or concave regions in the graph of the underlying density function. We define an abstract bump…
A typical computational geometry problem begins: Consider a set P of n points in R^d. However, many applications today work with input that is not precisely known, for example when the data is sensed and has some known error model. What if…
Reconstruction of sets from a random sample of points intimately related to them is the goal of set estimation theory. Within this context, a particular problem is the one related with the reconstruction of density level sets and…
We develop a simple Quantile Spacing (QS) method for accurate probabilistic estimation of one-dimensional entropy from equiprobable random samples, and compare it with the popular Bin-Counting (BC) method. In contrast to BC, which uses…
This paper introduces smoothed pseudo-population bootstrap methods for the purposes of variance estimation and the construction of confidence intervals for finite population quantiles. In an i.i.d. context, it has been shown that resampling…
The process comparing the empirical cumulative distribution function of the sample with a parametric estimate of the cumulative distribution function is known as the empirical process with estimated parameters and has been extensively…