Related papers: Implicit function density computation
A real arithmetic function f is multiplicatively monotonous if f (mn) -- f (m) has constant sign for m, n positive integers. Properties and examples of such functions are discussed, with applications to positive hermitian…
We consider distributions on $\mathbb{R}$ that can be written as the sum of a non-zero discrete distribution and an absolutely continuous distribution. We show that such a distribution is quasi-infinitely divisible if and only if its…
A classical problem of statistical inference is the valid specification of a model that can account for the statistical dependencies between observations when the true structure is dense, intractable, or unknown. To address this problem, a…
For a discrete function $f\left( x\right) $ on a discrete set, the finite difference can be either forward and backward. If $f\left( x\right) $ is a sum of two such functions $f\left( x\right) =f_{1}\left( x\right) +f_{2}\left( x\right) $,…
We consider how to use Hamiltonian Monte Carlo to sample from a distribution whose log-density is piecewise quadratic, conditioned on the sample lying on the level set of a piecewise affine, continuous function.
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
We study the problem of estimating the score function using both implicit score matching and denoising score matching. Assuming that the data distribution exhibiting a low-dimensional structure, we prove that implicit score matching is able…
We consider the statistical distribution of zeros of random meromorphic functions whose poles are independent random variables. It is demonstrated that correlation functions of these zeros can be computed analytically and explicit…
Dependency functions of dependent variables are relevant for i) performing uncertainty quantification and sensitivity analysis in presence of dependent variables and/or correlated variables, and ii) simulating random dependent variables. In…
Distribution functions for random variables that depend on a parameter are computed asymptotically for ensembles of positive Hermitian matrices. The inverse Fourier transform of the distribution is shown to be a Fredholm determinant of a…
This paper deals with the Fisher-consistency, weak continuity and differentiability of estimating functionals corresponding to a class of both linear and nonlinear regression high breakdown M estimates, which includes S and MM estimates. A…
Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A…
Elicitable functionals and (strictly) consistent scoring functions are of interest due to their utility of determining (uniquely) optimal forecasts, and thus the ability to effectively backtest predictions. However, in practice, assuming…
The problem of distributed function computation is studied, where functions to be computed is not necessarily symbol-wise. A new method to derive a converse bound for distributed computing is proposed; from the structure of functions to be…
Many nonlinear filters used in practise are stack filters. An algorithm is presented which calculates the output distribution of an arbitrary stack filter S from the disjunctive normal form (DNF) of its underlying positive Boolean function.…
We obtain the closed form expressions for the densities of the product, quotient, power and scalar multiple of independent stable subordinators. Similar results for the independent inverse stable subordinators are discussed. This is…
Posterior distribution over a countable set M of continuous data-sampling distributions piles up at L-projection of the true distribution r on M, provided that the L-projection is unique. If there are several L-projections of r on M, then…
We estimate density and regression functions for weak dependant datas. Using an exponential inequality obtained by Dedecker and Prieur and in a previous article of the author, we control the deviation between the estimator and the function…
We completely characterize $\Delta$- and local subexponentialities of positive-half compound Poisson distributions and extend the characterization on two-sided distributions. Moreover, $\Delta$-subexponentiality of infinitely divisible…
This work builds on our recent work on a distributed optimization algorithm for graphs with directed unreliable communications. We show its linear convergence when we take either the proximal of each function or an affine minorant for when…