NEAREST-NEIGHBOR ENTROPY ESTIMATORS WITH WEAK METRICS

被引：1
|
作者：
Timofeev, Evgeniy [1 ]
Kaltchenko, Alexei [2 ]
机构：
[1] Yaroslavl State Univ, Dept Comp Sci, Yaroslavl, Russia
[2] Wilfrid Laurier Univ, Dept Phys & Comp Sci, Waterloo, ON N2L 3C5, Canada
来源：
ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2014年 / 8卷 / 02期
关键词：
Entropy; stochastic process; stationary; estimation; nonparametric; nearest neighbor; bias; metric; CONVERGENCE; SEQUENCES;
D O I：
10.3934/amc.2014.8.119
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
A problem of improving the accuracy of nonparametric entropy estimation for a stationary ergodic process is considered. New weak metrics are introduced and relations between metrics, measures, and entropy are discussed. A new nonparametric entropy estimator is constructed based on weak metrics and has a parameter with which the estimator is optimized to reduce its bias. It is shown that estimator's variance is upper-bounded by a nearly optimal Cramer-Rao lower bound.
引用
收藏
页码：119 / 127
页数：9
相关论文
共 50 条
  • [1] Selection of a Metric for the Nearest Neighbor Entropy Estimators
    Timofeev E.
    Journal of Mathematical Sciences, 2014, 203 (6) : 892 - 906
  • [2] ASYMPTOTIC NORMALITY OF PARAMETER ESTIMATORS FOR SOME NEAREST-NEIGHBOR MODELS
    DOBEK, A
    BIOMETRICAL JOURNAL, 1994, 36 (01) : 103 - 108
  • [3] THE LAW OF THE ITERATED LOGARITHM FOR THE MULTIVARIATE NEAREST-NEIGHBOR DENSITY ESTIMATORS
    RALESCU, SS
    JOURNAL OF MULTIVARIATE ANALYSIS, 1995, 53 (01) : 159 - 179
  • [4] Learning weighted metrics to minimize nearest-neighbor classification error
    Paredes, R
    Vidal, E
    IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 2006, 28 (07) : 1100 - 1110
  • [5] K n-nearest neighbor estimators of entropy
    Mnatsakanov R.M.
    Misra N.
    Li S.
    Harner E.J.
    Mathematical Methods of Statistics, 2008, 17 (3) : 261 - 277
  • [6] Efficiency of nearest neighbor entropy estimators for Bernoulli measures
    Timofeev, Evgeniy A.
    Kaltchenko, Alexei
    INDEPENDENT COMPONENT ANALYSES, COMPRESSIVE SAMPLING, WAVELETS, NEURAL NET, BIOSYSTEMS, AND NANOENGINEERING XII, 2014, 9118
  • [7] ON NEAREST-NEIGHBOR GRAPHS
    PATERSON, MS
    YAO, FF
    LECTURE NOTES IN COMPUTER SCIENCE, 1992, 623 : 416 - 426
  • [8] On Nearest-Neighbor Graphs
    D. Eppstein
    M. S. Paterson
    F. F. Yao
    Discrete & Computational Geometry, 1997, 17 : 263 - 282
  • [9] Nearest-neighbor methods
    Sutton, Clifton
    WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL STATISTICS, 2012, 4 (03): : 307 - 309
  • [10] On nearest-neighbor graphs
    Eppstein, D
    Paterson, MS
    Yao, FF
    DISCRETE & COMPUTATIONAL GEOMETRY, 1997, 17 (03) : 263 - 282
12345