
Invariant density adaptive estimation for ergodic jump diffusion processes over anisotropic classes
We consider the solution X = (Xt) t>0 of a multivariate stochastic diffe...
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Level set and density estimation on manifolds
Given an iid sample of a distribution supported on a smooth manifold M^d...
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Modeling a Hidden Dynamical System Using Energy Minimization and Kernel Density Estimates
In this paper we develop a kernel density estimation (KDE) approach to m...
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Bestscored Random Forest Density Estimation
This paper presents a brand new nonparametric density estimation strateg...
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Simulating deformable objects for computer animation: a numerical perspective
We examine a variety of numerical methods that arise when considering dy...
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Mixing it up: A general framework for Markovian statistics beyond reversibility and the minimax paradigm
Up to now, the nonparametric analysis of multidimensional continuoustim...
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Kernel Density Estimation Bias under Minimal Assumptions
Kernel Density Estimation is a very popular technique of approximating a...
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Kernel Density Estimation for Dynamical Systems
We study the density estimation problem with observations generated by certain dynamical systems that admit a unique underlying invariant Lebesgue density. Observations drawn from dynamical systems are not independent and moreover, usual mixing concepts may not be appropriate for measuring the dependence among these observations. By employing the Cmixing concept to measure the dependence, we conduct statistical analysis on the consistency and convergence of the kernel density estimator. Our main results are as follows: First, we show that with properly chosen bandwidth, the kernel density estimator is universally consistent under L_1norm; Second, we establish convergence rates for the estimator with respect to several classes of dynamical systems under L_1norm. In the analysis, the density function f is only assumed to be Hölder continuous which is a weak assumption in the literature of nonparametric density estimation and also more realistic in the dynamical system context. Last but not least, we prove that the same convergence rates of the estimator under L_∞norm and L_1norm can be achieved when the density function is Hölder continuous, compactly supported and bounded. The bandwidth selection problem of the kernel density estimator for dynamical system is also discussed in our study via numerical simulations.
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