Paper Info
Title
Kernel Density Estimation for Dynamical Systems.
Abstract
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 C-mixing 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-1-norm; Second, we establish convergence rates for the estimator with respect to several classes of dynamical systems under L-1-norm. In the analysis, the density function f is only assumed to be Holder continuous or pointwise Holder controllable 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-infinity-norm and L-1-norm can be achieved when the density function is Holder 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.
Year
Venue
Keywords
2018
JOURNAL OF MACHINE LEARNING RESEARCH
Kernel density estimation,dynamical system,dependent observations,C-mixing process,universal consistency,convergence rates,covering number,learning theory
Field
DocType
Volume
Pattern recognition,Algorithm,Dynamical systems theory,Artificial intelligence,Mathematics,Kernel density estimation
Journal
19
Issue
ISSN
Citations 
35
1532-4435
0
PageRank 
References 
Authors
0.34
4
4
Name
Order
Citations
PageRank
Hanyuan Hang1111.84
I. Steinwart2939.78
Yun-long Feng312511.69
J. A. Suykens4305.97