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Denoising Manifolds for Dimension

Jammalamadaka, Arvind K. (2009)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 68T01, 62H30, 32C09.Locally Linear Embedding (LLE) has gained prominence as a tool in unsupervised non-linear dimensional reduction. While the algorithm aims to preserve certain proximity relations between the observed points, this may not always be desirable if the shape in higher dimensions that we are trying to capture is observed with noise. This note suggests that a desirable first step is to remove or at least reduce the noise in the observations before...

Densities of determinant ratios, their moments and some simultaneous confidence intervals in the multivariate Gauss-Markoff model

Wiktor Oktaba (1995)

Applications of Mathematics

The following three results for the general multivariate Gauss-Markoff model with a singular covariance matrix are given or indicated. 1 ∘ determinant ratios as products of independent chi-square distributions, 2 ∘ moments for the determinants and 3 ∘ the method of obtaining approximate densities of the determinants.

Density deconvolution with associated stationary data

Le Thi Hong Thuy, Cao Xuan Phuong (2023)

Applications of Mathematics

We study the density deconvolution problem when the random variables of interest are an associated strictly stationary sequence and the random noises are i.i.d. with a nonstandard density. Based on a nonparametric strategy, we introduce an estimator depending on two parameters. This estimator is shown to be consistent with respect to the mean integrated squared error. Under additional regularity assumptions on the target function as well as on the density of noises, some error estimates are derived....

Density estimation with quadratic loss: a confidence intervals method

Pierre Alquier (2008)

ESAIM: Probability and Statistics

We propose a feature selection method for density estimation with quadratic loss. This method relies on the study of unidimensional approximation models and on the definition of confidence regions for the density thanks to these models. It is quite general and includes cases of interest like detection of relevant wavelets coefficients or selection of support vectors in SVM. In the general case, we prove that every selected feature actually improves the performance of the estimator. In the case...

Density smoothness estimation problem using a wavelet approach

Karol Dziedziul, Bogdan Ćmiel (2014)

ESAIM: Probability and Statistics

In this paper we consider a smoothness parameter estimation problem for a density function. The smoothness parameter of a function is defined in terms of Besov spaces. This paper is an extension of recent results (K. Dziedziul, M. Kucharska, B. Wolnik, Estimation of the smoothness parameter). The construction of the estimator is based on wavelets coefficients. Although we believe that the effective estimation of the smoothness parameter is impossible in general case, we can show that it becomes...

Dependence Measuring from Conditional Variances

Noppadon Kamnitui, Tippawan Santiwipanont, Songkiat Sumetkijakan (2015)

Dependence Modeling

A conditional variance is an indicator of the level of independence between two random variables. We exploit this intuitive relationship and define a measure v which is almost a measure of mutual complete dependence. Unsurprisingly, the measure attains its minimum value for many pairs of non-independent ran- dom variables. Adjusting the measure so as to make it invariant under all Borel measurable injective trans- formations, we obtain a copula-based measure of dependence v* satisfying A. Rényi’s...

Dependence of Stock Returns in Bull and Bear Markets

Jadran Dobric, Gabriel Frahm, Friedrich Schmid (2013)

Dependence Modeling

Despite of its many shortcomings, Pearson’s rho is often used as an association measure for stock returns. A conditional version of Spearman’s rho is suggested as an alternative measure of association. This approach is purely nonparametric and avoids any kind of model misspecification. We derive hypothesis tests for the conditional rank-correlation coefficients particularly arising in bull and bear markets and study their finite-sample performance by Monte Carlo simulation. Further, the daily returns...

Dependent Lindeberg central limit theorem and some applications

Jean-Marc Bardet, Paul Doukhan, Gabriel Lang, Nicolas Ragache (2008)

ESAIM: Probability and Statistics

In this paper, a very useful lemma (in two versions) is proved: it simplifies notably the essential step to establish a Lindeberg central limit theorem for dependent processes. Then, applying this lemma to weakly dependent processes introduced in Doukhan and Louhichi (1999), a new central limit theorem is obtained for sample mean or kernel density estimator. Moreover, by using the subsampling, extensions under weaker assumptions of these central limit theorems are provided. All the usual causal...

Design of a model following control system for nonlinear descriptor system in discrete time

Shujing Wu, Shigenori Okubo, Dazhong Wang (2008)

Kybernetika

A model following control system (MFCS) can output general signals following the desired ones. In this paper, a method of nonlinear MFCS will be extended to be a nonlinear descriptor system in discrete time. The nonlinear system studied in this paper has the property of norm constraint | | f ( v ( k ) ) | | ≤ α + β | | v ( k ) | | γ , where α ≥ 0 , β ≥ 0 , 0 ≤ γ < 1 . In this case, a new criterion is proposed to ensure the internal states be stable.

Detección de rasgos en imágenes binarias mediante procesos puntuales espaciales marcados.

Jorge Mateu, Gil Lorenzo (2002)

Qüestiió

En este trabajo consideramos el problema de la detección de rasgos bajo la presencia de ruido en imágenes que tras un cierto tratamiento se reducen a binarias, por la presencia de dos tipos de elementos. Podemos encontrar ejemplos de este problema en la detección de minas por medio de imágenes de avión o satélite, en la búsqueda de rasgos en imágenes microscópicas de células, o en la caracterización de fallas en zonas de terremotos.En primer lugar revisamos algunos métodos de detección jerárquicos...

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