Geodesic
Selection of a~metric for the nearest neighbor entropy estimators
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 2, pp. 209-227

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We consider the problem of improving the efficiency of the nonparametric entropy estimation for a stationary ergodic process. Our approach is based on the nearest-neighbor distances. We propose a broad class of metrics on the space of right-sided infinite sequences drawn from a finite alphabet. The new metric has a parameter which is a nonincreasing function. We prove that, under certain conditions, our estimators have a small variance and show that a special selection of the metric parameters reduces the estimator's bias. 
@article{FPM_2013_18_2_a16,
     author = {E. A. Timofeev},
     title = {Selection of a~metric for the nearest neighbor entropy estimators},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {209--227},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2013_18_2_a16/}
}
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E. A. Timofeev. Selection of a~metric for the nearest neighbor entropy estimators. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 2, pp. 209-227. http://geodesic.mathdoc.fr/item/FPM_2013_18_2_a16/