TY - JOUR

T1 - Non-linear kernel density estimation for binned data: convergence in entropy.

AU - Blower, Gordon

AU - Kelsall, Julia E.

PY - 2002

Y1 - 2002

N2 - 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 L1\, and transportation metrics. The proof uses a logarithmic Sobolev inequality comparing relative Shannon entropy and relative Fisher information with respect to \hat f.

AB - 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 L1\, and transportation metrics. The proof uses a logarithmic Sobolev inequality comparing relative Shannon entropy and relative Fisher information with respect to \hat f.

KW - binned data

KW - density estimation

KW - kernel estimation

KW - logarithmic Sobolev inequality

KW - transportation

M3 - Journal article

VL - 8

SP - 423

EP - 449

JO - Bernoulli

JF - Bernoulli

SN - 1350-7265

IS - 4

ER -