Related papers: Smoothed Analysis of Moore-Penrose Inversion
This work examines under what circumstances adaptivity for truncated SVD estimation can be achieved by an early stopping rule based on the smoothed residuals $ \| ( A A^{\top} )^{\alpha / 2} ( Y - A \hat{\mu}^{( m )}) \|^{2} $. Lower and…
In the literature, quite a few measures have been proposed for quantifying the deviation of a probability distribution from symmetry. The most popular of these skewness measures are based on the third centralized moment and on quantiles.…
Computing smoothing distributions, the distributions of one or more states conditional on past, present, and future observations is a recurring problem when operating on general hidden Markov models. The aim of this paper is to provide a…
The work treats smoothing and dispersive properties of solutions to the Schrodinger equation with magnetic potential. Under suitable smallness assumption on the potential involving scale invariant norms we prove smoothing - Strichartz…
In an earlier paper, we discussed the probability that the determinant of a matrix undergoes the least change upon perturbation of one of its elements, provided that most or all of the elements of the matrix are chosen at random and that…
Testing procedures for assessing specific parametric model forms, or for checking the plausibility of simplifying assumptions, play a central role in the mathematical treatment of the uncertain. No certain answers are obtained by testing…
Shrinkage estimators of covariance are an important tool in modern applied and theoretical statistics. They play a key role in regularized estimation problems, such as ridge regression (aka Tykhonov regularization), regularized discriminant…
We discuss the practice of directly or indirectly assuming a model for the number of points when modelling spatial point patterns even though it is rarely possible to validate such a model in practice since most point pattern data consist…
In the first part of the paper, we study the inversion statistic of random permutations under the family $(\mathbb{P}_\theta^{(n)})_{\theta \ge 0}$ of Ewens sampling distributions on $S_n$. We obtain a rather simple exact formula for the…
For the extended skew-normal distribution, which represents an extension of the normal (or Gaussian) distribution, we focus on the properties of the log-likelihood function and derived quantities in the the bivariate case. Specifically, we…
In this paper, we consider the problem of controlling a partially observed Markov decision process (POMDP) in order to actively estimate its state trajectory over a fixed horizon with minimal uncertainty. We pose a novel active smoothing…
Expectile regression is a nice tool for investigating conditional distributions beyond the conditional mean. It is well-known that expectiles can be described with the help of the asymmetric least square loss function, and this link makes…
This paper introduces a smoothed proximal Lagrangian method for minimizing a nonconvex smooth function over a convex domain with additional explicit convex nonlinear constraints. Two key features are 1) the proposed method is single-looped,…
This paper presents a procedure for testing the hypothesis that the underlying distribution of the data is elliptical when using robust location and scatter estimators instead of the sample mean and covariance matrix. Under mild assumptions…
We extend nonparametric regression smoothing splines to a context where there is endogeneity and instrumental variables are available. Unlike popular existing estimators, the resulting estimator is one-step and relies on a unique…
I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…
The condition number of a differentiable convex function, namely the ratio of its smoothness to strong convexity constants, is closely tied to fundamental properties of the function. In particular, the condition number of a quadratic convex…
We consider a non-parametric Bayesian model for conditional densities. The model is a finite mixture of normal distributions with covariate dependent multinomial logit mixing probabilities. A prior for the number of mixture components is…
We study the distribution of entries of a random permutation matrix under a "randomized basis," i.e., we conjugate the random permutation matrix by an independent random orthogonal matrix drawn from Haar measure. It is shown that under…
We derive bounds for the minimum and maximum eigenvalues and the spectral condition number of matrices for isogeometric discretizations of elliptic partial differential equations in an open, bounded, simply connected Lipschitz domain…