Anisotropic adaptive kernel deconvolution

F. Comte; C. Lacour

Displaying similar documents to “Anisotropic adaptive kernel deconvolution”

Local percolative properties of the vacant set of random interlacements with small intensity

Alexander Drewitz, Balázs Ráth, Artëm Sapozhnikov (2014)

Annales de l'I.H.P. Probabilités et statistiques

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Random interlacements at level $u$ is a one parameter family of connected random subsets of $ℤ^{d}$ , $d \geq 3$ ( (2010) 2039–2087). Its complement, the vacant set at level $u$ , exhibits a non-trivial percolation phase transition in $u$ ( (2009) 831–858; (2010) 2039–2087), and the infinite connected component, when it exists, is almost surely unique ( (2009) 454–466). In this paper we study local percolative properties of the vacant set of random...

Spatially adaptive density estimation by localised Haar projections

Florian Gach, Richard Nickl, Vladimir Spokoiny (2013)

Annales de l'I.H.P. Probabilités et statistiques

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Given a random sample from some unknown density $f_{0} : ℝ \to [0, \infty)$ we devise Haar wavelet estimators for $f_{0}$ with variable resolution levels constructed from localised test procedures (as in Lepski, Mammen and Spokoiny ( (1997) 927–947)). We show that these estimators satisfy an oracle inequality that adapts to heterogeneous smoothness of $f_{0}$ , simultaneously for every point $x$ in a fixed interval, in sup-norm loss. The thresholding constants involved in the test procedures can be chosen in...

The category of compactifications and its coreflections

Anthony W. Hager, Brian Wynne (2022)

Commentationes Mathematicae Universitatis Carolinae

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We define “the category of compactifications”, which is denoted , and consider its family of coreflections, denoted . We show that is a complete lattice with bottom the identity and top an interpretation of the Čech–Stone $β$ . A $c \in$ implies the assignment to each locally compact, noncompact $Y$ a compactification minimum for membership in the “object-range” of $c$ . We describe the minimum proper compactifications of locally compact, noncompact spaces, show that these generate...

Superdiffusivity for brownian motion in a poissonian potential with long range correlation I: Lower bound on the volume exponent

Hubert Lacoin (2012)

Annales de l'I.H.P. Probabilités et statistiques

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We study trajectories of $d$ -dimensional Brownian Motion in Poissonian potential up to the hitting time of a distant hyper-plane. Our Poissonian potential $V$ is constructed from a field of traps whose centers location is given by a Poisson Point Process and whose radii are IID distributed with a common distribution that has unbounded support; it has the particularity of having long-range correlation. We focus on the case where the law of the trap radii $ν$ has power-law decay and prove that...

Existence, Consistency and computer simulation for selected variants of minimum distance estimators

Václav Kůs, Domingo Morales, Jitka Hrabáková, Iva Frýdlová (2018)

Kybernetika

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The paper deals with sufficient conditions for the existence of general approximate minimum distance estimator (AMDE) of a probability density function $f_{0}$ on the real line. It shows that the AMDE always exists when the bounded $φ$ -divergence, Kolmogorov, Lévy, Cramér, or discrepancy distance is used. Consequently, $n^{- 1 / 2}$ consistency rate in any bounded $φ$ -divergence is established for Kolmogorov, Lévy, and discrepancy estimators under the condition that the degree of variations of the corresponding...

Strong $𝐗$ -robustness of interval max-min matrices

Helena Myšková, Ján Plavka (2021)

Kybernetika

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In max-min algebra the standard pair of operations plus and times is replaced by the pair of operations maximum and minimum, respectively. A max-min matrix $A$ is called strongly robust if the orbit $x, A \otimes x, A^{2} \otimes x, \dots$ reaches the greatest eigenvector with any starting vector. We study a special type of the strong robustness called the strong -robustness, the case that a starting vector is limited by a lower bound vector and an upper bound vector. The equivalent condition...

Convergence rates for the full gaussian rough paths

Peter Friz, Sebastian Riedel (2014)

Annales de l'I.H.P. Probabilités et statistiques

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Under the key assumption of finite $ρ$ -variation, $ρ \in [1, 2)$ , of the covariance of the underlying Gaussian process, sharp a.s. convergence rates for approximations of Gaussian rough paths are established. When applied to Brownian resp. fractional Brownian motion (fBM), $ρ = 1$ resp. $ρ = 1 / (2 H)$ , we recover and extend the respective results of ( (2009) 2689–2718) and ( (2012) 518–550). In particular, we establish an a.s. rate $k^{- (1 / ρ - 1 / 2 - ε)}$ , any $ε g t; 0$ , for Wong–Zakai and Milstein-type approximations...

$M$ -estimators of structural parameters in pseudolinear models

Friedrich Liese, Igor Vajda (1999)

Applications of Mathematics

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Real valued $M$ -estimators ${\hat{θ}}_{n} : = min \sum_{1}^{n} ρ (Y_{i} - τ (θ))$ in a statistical model with observations $Y_{i} \sim F_{θ_{0}}$ are replaced by $ℝ^{p}$ -valued $M$ -estimators ${\hat{β}}_{n} : = min \sum_{1}^{n} ρ (Y_{i} - τ (u (z_{i}^{T} β)))$ in a new model with observations $Y_{i} \sim F_{u (z_{i}^{t} β_{0})}$ , where $z_{i} \in ℝ^{p}$ are regressors, $β_{0} \in ℝ^{p}$ is a structural parameter and $u : ℝ \to ℝ$ a structural function of the new model. Sufficient conditions for the consistency of ${\hat{β}}_{n}$ are derived, motivated by the sufficiency conditions for the simpler “parent estimator” ${\hat{θ}}_{n}$ . The result is a general method of consistent estimation in a class of nonlinear (pseudolinear) statistical...

New stability results for spheres and Wulff shapes

Julien Roth (2018)

Communications in Mathematics

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We prove that a closed convex hypersurface of the Euclidean space with almost constant anisotropic first and second mean curvatures in the $L^{p}$ -sense is $W^{2, p}$ -close (up to rescaling and translations) to the Wulff shape. We also obtain characterizations of geodesic hyperspheres of space forms improving those of [] and [].

Rank theory approach to ridge, LASSO, preliminary test and Stein-type estimators: Comparative study

A. K. Md. Ehsanes Saleh, Radim Navrátil (2018)

Kybernetika

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In the development of efficient predictive models, the key is to identify suitable predictors for a given linear model. For the first time, this paper provides a comparative study of ridge regression, LASSO, preliminary test and Stein-type estimators based on the theory of rank statistics. Under the orthonormal design matrix of a given linear model, we find that the rank based ridge estimator outperforms the usual rank estimator, restricted R-estimator, rank-based LASSO, preliminary...

Adaptive estimation of a density function using beta kernels

Karine Bertin, Nicolas Klutchnikoff (2014)

ESAIM: Probability and Statistics

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In this paper we are interested in the estimation of a density − defined on a compact interval of ℝ− from independent and identically distributed observations. In order to avoid boundary effect, beta kernel estimators are used and we propose a procedure (inspired by Lepski’s method) in order to select the bandwidth. Our procedure is proved to be adaptive in an asymptotically minimax framework. Our estimator is compared with both the cross-validation algorithm and the oracle estimator...

Ergodic behaviour of “signed voter models”

G. Maillard, T. S. Mountford (2013)

Annales de l'I.H.P. Probabilités et statistiques

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We answer some questions raised by Gantert, Löwe and Steif ( (2005) 767–780) concerning “signed” voter models on locally finite graphs. These are voter model like processes with the difference that the edges are considered to be either positive or negative. If an edge between a site $x$ and a site $y$ is negative (respectively positive) the site $y$ will contribute towards the flip rate of $x$ if and only if the two current spin values are equal (respectively opposed). ...

Localization and delocalization for heavy tailed band matrices

Florent Benaych-Georges, Sandrine Péché (2014)

Annales de l'I.H.P. Probabilités et statistiques

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We consider some random band matrices with band-width $N^{μ}$ whose entries are independent random variables with distribution tail in $x^{- α}$ . We consider the largest eigenvalues and the associated eigenvectors and prove the following phase transition. On the one hand, when $α l t; 2 (1 + μ^{- 1})$ , the largest eigenvalues have order $N^{(1 + μ) / α}$ , are asymptotically distributed as a Poisson process and their associated eigenvectors are essentially carried by two coordinates (this phenomenon has already been remarked for full matrices...