Bernoulli
- Bernoulli
- Volume 8, Number 4 (2002), 423-449.
Nonlinear kernel density estimation for binned data: convergence in entropy
Gordon Blower and Julia E. Kelsall
Abstract
A method is proposed for creating a smooth kernel density estimate from a sample of binned data. Simulations indicate that this method produces an estimate for relatively finely binned data which is close to what one would obtain using the original unbinned data. The kernel density estimate $\hat {f}$, is the stationary distribution of a Markov process resembling the Ornstein-Uhlenbeck process. This $\hat {f}$, may be found by an iteration scheme which converges at a geometric rate in the entropy pseudo-metric, and hence in $L^1$, and transportation metrics. The proof uses a logarithmic Sobolev inequality comparing relative Shannon entropy and relative Fisher information with respect to $\hat {f}$.
Article information
Source
Bernoulli Volume 8, Number 4 (2002), 423-449.
Dates
First available in Project Euclid: 7 March 2004
Permanent link to this document
http://projecteuclid.org/euclid.bj/1078681378
Mathematical Reviews number (MathSciNet)
MR2003d:62101
Zentralblatt MATH identifier
1006.62030
Keywords
binned data density estimation kernel estimation logarithmic Sobolev inequality transportation
Citation
Blower, Gordon; Kelsall, Julia E. Nonlinear kernel density estimation for binned data: convergence in entropy. Bernoulli 8 (2002), no. 4, 423--449. http://projecteuclid.org/euclid.bj/1078681378.
