Consistency of the kernel density estimator: a survey

Wied, Dominik; Weißbach, Rafael

doi:10.1007/s00362-010-0338-1

Cited by 66 publications

(34 citation statements)

References 29 publications

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“…An asymptotic view reveals this strength: with an infinite amount of data, a non-parametric model will converge almost sure to the true distribution (Wied and Weißbach, 2012). In contrast, parametric models lack this property.…”

Section: Critical Discussion Of the Non-parametric Modelmentioning

confidence: 99%

Virtual sensor models for real-time applications

et al. 2016

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Abstract. Increased complexity and severity of future driver assistance systems demand extensive testing and validation. As supplement to road tests, driving simulations offer various benefits. For driver assistance functions the perception of the sensors is crucial. Therefore, sensors also have to be modeled. In this contribution, a statistical data-driven sensormodel, is described. The state-space based method is capable of modeling various types behavior. In this contribution, the modeling of the position estimation of an automotive radar system, including autocorrelations, is presented. For rendering real-time capability, an efficient implementation is presented.

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Section: Critical Discussion Of the Non-parametric Modelmentioning

confidence: 99%

Virtual sensor models for real-time applications

et al. 2016

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“…Under assumptions (I 2 ) − (I 4 ) given in the Appendix, it is obtained that π(x, y) → π(x, y) a.s.; see Einmahl & Mason (2005), Rao (2009) and Wied & Weißbach (2012). From assumption (I 5 ), we have, β 0 = Argmin β∈B lim n→∞ E{D n (β)}.…”

Section: Weighted Empirical Likelihood Rank Based Inferencementioning

confidence: 98%

“…Assumptions (I 2 ) − (I 4 ) are necessary to ensure the result in Theorem 2; see Einmahl & Mason (2005), Rao (2009) and Wied & Weißbach (2012). The identifiability condition (I 5 ) is a key to ensure the strong consistency of the rank-based estimator; see Bindele (2017).…”

Section: Assumptionsmentioning

confidence: 99%

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Rank-based estimating equation with non-ignorable missing responses via empirical likelihood

Bindele¹,

Zhao²

2018

STAT SINICA

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In this paper, a general regression model with responses missing not at random is considered. From a rankbased estimating equation, a rank-based estimator of the regression parameter is derived. Based on this estimator's asymptotic normality property, a consistent sandwich estimator of its corresponding asymptotic covariance matrix is obtained. In order to overcome the over-coverage issue of the normal approximation procedure, the empirical likelihood based on the rank-based gradient function is defined, and its asymptotic distribution is established. Extensive simulation experiments under different settings of error distributions with different response probabilities are considered, and the simulation results show that the proposed empirical likelihood approach has better performance in terms of coverage probability and average length of confidence intervals for the regression parameters compared with the normal approximation approach and its least-squares counterpart. A real data example is provided to illustrate the proposed methods.

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“…See [27,58] for the convergence analysis of KDE. However, we note that for a finite set of samples, KDE can be prone to errors, especially for high-dimensional data.…”

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confidence: 99%

A Domain Decomposition Approach for Uncertainty Analysis

Liao¹,

Willcox²

2015

SIAM J. Sci. Comput.

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Abstract. This paper proposes a decomposition approach for uncertainty analysis of systems governed by partial differential equations (PDEs). The system is split into local components using domain decomposition. Our domain-decomposed uncertainty quantification (DDUQ) approach performs uncertainty analysis independently on each local component in an "offline" phase, and then assembles global uncertainty analysis results using precomputed local information in an "online" phase. At the heart of the DDUQ approach is importance sampling, which weights the precomputed local PDE solutions appropriately so as to satisfy the domain decomposition coupling conditions. To avoid global PDE solves in the online phase, a proper orthogonal decomposition reduced model provides an efficient approximate representation of the coupling functions. 1. Introduction. Many problems arising in computational science and engineering are described by mathematical models of high complexity-involving multiple disciplines, characterized by a large number of parameters, and impacted by multiple sources of uncertainty. Decomposition of a system into subsystems or component parts has been one strategy to manage this complexity. For example, modern engineered systems are typically designed by multiple groups, usually decomposed along disciplinary or subsystem lines, sometimes spanning different organizations and even different geographical locations. Mathematical strategies have been developed for decomposing a simulation task (e.g., domain decomposition methods [45]), for decomposing an optimization task (e.g., domain decomposition for optimal design or control [28,10,29,5]), and for decomposing a complex design task (e.g., decomposition approaches to multidisciplinary optimization [15,34,55]). In this paper we propose a decomposition approach for uncertainty quantification (UQ). In particular, we focus on the simulation of systems governed by stochastic partial differential equations (PDEs) and a domain decomposition approach to quantification of uncertainty in the corresponding quantities of interest.In the design setting, decomposition approaches are not typically aimed at improving computational efficiency, although in some cases decomposition can admit parallelism that would otherwise be impossible [57]. Rather, decomposition is typically employed in situations for which it is infeasible or impractical to achieve tight coupling among the system subcomponents. This inability to achieve tight coupling becomes a particular problem when the goal is to wrap an outer loop (e.g., optimization) around the simulation. In the field of multidisciplinary design optimization (MDO), decomposition is achieved through mathematical formulations such as col-

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Consistency of the kernel density estimator: a survey

Cited by 66 publications

References 29 publications

Virtual sensor models for real-time applications

Virtual sensor models for real-time applications

Rank-based estimating equation with non-ignorable missing responses via empirical likelihood

A Domain Decomposition Approach for Uncertainty Analysis

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