Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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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 -