Nonparametric estimation of quantile-based entropy function

In this article, we propose three nonparametric estimators for quantile-based Shannon differential entropy function for complete samples. Asymptotic properties of the estimators are established und...

[1]  Michael Falk,et al.  On the estimation of the quantile density function , 1986 .

[2]  Sana S BuHamra,et al.  Inference concerning quantile for left truncated and right censored data , 2004, Comput. Stat. Data Anal..

[4]  Isha Dewan,et al.  Nonparametric estimation of quantile density function , 2012, Comput. Stat. Data Anal..

[5]  N. Ebrahimi,et al.  Two measures of sample entropy , 1994 .

[6]  Oldrich A Vasicek,et al.  A Test for Normality Based on Sample Entropy , 1976 .

[7]  Robert Wieczorkowski,et al.  Entropy estimators‐improvements and comparisons , 1999 .

[8]  P. G. Sankaran,et al.  Quantile-based cumulative entropies , 2017 .

[9]  P. G. Sankaran,et al.  Rényi’s residual entropy: A quantile approach , 2014 .

[10]  P. Hall,et al.  On the estimation of entropy , 1993 .

[11]  S. Sunoj,et al.  Quantile based entropy function , 2012 .

[12]  S. Bouzebda,et al.  New Kernel-type estimator of Shanonnʼs entropy , 2014 .

[13]  G. Roussas,et al.  Smooth estimate of quantiles under association , 1997 .

[14]  Robin K. S. Hankin,et al.  A NEW FAMILY OF NON‐NEGATIVE DISTRIBUTIONS , 2006 .

[15]  A. H. Khammar,et al.  Quantile based Tsallis entropy in residual lifetime , 2018 .

[16]  G. Basharin On a Statistical Estimate for the Entropy of a Sequence of Independent Random Variables , 1959 .

[17]  Shie-Shien Yang A Smooth Nonparametric Estimator of a Quantile Function , 1985 .

[18]  Magne Vollan Aarset,et al.  How to Identify a Bathtub Hazard Rate , 1987, IEEE Transactions on Reliability.

[19]  A. Khammar,et al.  A quantile-based generalized dynamic cumulative measure of entropy , 2018 .

[20]  Hadi Alizadeh Noughabi,et al.  A NEW ESTIMATOR OF ENTROPY , 2010 .

[21]  S. Sunoj,et al.  Quantile-Based Entropy of Order Statistics , 2017 .

[22]  M. C. Jones,et al.  A reliable data-based bandwidth selection method for kernel density estimation , 1991 .

[23]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[24]  Juan C. Correa A new estimator of entropy , 1995 .

[25]  E. Parzen Nonparametric Statistical Data Modeling , 1979 .

[26]  Rajiv Nandan Rai,et al.  Repairable Systems Reliability Analysis: A Comprehensive Framework , 2020 .

[27]  W. J. Padgett A Kernel-Type Estimator of a Quantile Function from Right-Censored Data , 1986 .

[28]  Ibrahim A. Ahmad,et al.  A nonparametric estimation of the entropy for absolutely continuous distributions (Corresp.) , 1976, IEEE Trans. Inf. Theory.

[29]  P. Sankaran,et al.  The Govindarajulu Distribution: Some Properties and Applications , 2012 .

[30]  Thomas Schürmann Bias analysis in entropy estimation , 2004 .

[31]  M. C. Jones Estimating densities, quantiles, quantile densities and density quantiles , 1992 .

[32]  Hwa-Lung Yu,et al.  Quantile-based Bayesian maximum entropy approach for spatiotemporal modeling of ambient air quality levels. , 2013, Environmental science & technology.

[33]  Quantile-based reliability aspects of cumulative Tsallis entropy in past lifetime , 2018, Metrika.

[34]  Alexander Bulinski,et al.  Statistical Estimation of the Shannon Entropy , 2018, Acta Mathematica Sinica, English Series.