scholarly journals Shannon Entropy Estimation for Linear Processes

2020 ◽  
Vol 13 (9) ◽  
pp. 205
Author(s):  
Timothy Fortune ◽  
Hailin Sang
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Shannon Entropy ◽  
Kernel Density ◽  
Linear Process ◽  
Kernel Density Estimator ◽  
Density Estimator ◽  
Linear Processes ◽  
Entropy Estimation

In this paper, we estimate the Shannon entropy S(f)=−E[log(f(x))] of a one-sided linear process with probability density function f(x). We employ the integral estimator Sn(f), which utilizes the standard kernel density estimator fn(x) of f(x). We show that Sn(f) converges to S(f) almost surely and in Ł2 under reasonable conditions.

Rate of Convergence in Density Estimation Using Neural Networks

1996 ◽  
Vol 8 (5) ◽  
pp. 1107-1122 ◽  
Author(s):  
Dharmendra S. Modha ◽  
Elias Masry
Keyword(s):  
Neural Networks ◽  
Probability Density Function ◽  
Probability Density ◽  
Rate Of Convergence ◽  
Density Function ◽  
Density Estimation ◽  
Exponential Family ◽  
Density Estimator ◽  
Estimation Scheme ◽  
Hidden Layer

Given N i.i.d. observations {Xi}Ni=1 taking values in a compact subset of Rd, such that p* denotes their common probability density function, we estimate p* from an exponential family of densities based on single hidden layer sigmoidal networks using a certain minimum complexity density estimation scheme. Assuming that p* possesses a certain exponential representation, we establish a rate of convergence, independent of the dimension d, for the expected Hellinger distance between the proposed minimum complexity density estimator and the true underlying density p*.

scholarly journals A numerical study of entropy and residual entropy estimators based on smooth density estimators for non-negative random variables

2021 ◽  
Vol 54 (2) ◽  
pp. 99-121
Author(s):  
Yogendra P. Chaubey ◽  
Nhat Linh Vu
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Numerical Study ◽  
Random Variables ◽  
Random Variable ◽  
Residual Entropy ◽  
Density Estimator ◽  
Wide Range ◽  
Smooth Density

In this paper, we are interested in estimating the entropy of a non-negative random variable. Since the underlying probability density function is unknown, we propose the use of the Poisson smoothed histogram density estimator to estimate the entropy. To study the per- formance of our estimator, we run simulations on a wide range of densities and compare our entropy estimators with the existing estimators based on different approaches such as spacing estimators. Furthermore, we extend our study to residual entropy estimators which is the entropy of a random variable given that it has been survived up to time $t$.

Structural health monitoring by probability density function of autoregressive-based damage features and fast distance correlation method

2021 ◽  
pp. 107754632110201
Author(s):  
Mohammad Ali Heravi ◽  
Seyed Mehdi Tavakkoli ◽  
Alireza Entezami
Keyword(s):  
Time Series ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Large Scale ◽  
Hypothesis Test ◽  
Correlation Method ◽  
Model Parameters ◽  
Density Estimator ◽  
Distance Correlation

In this article, the autoregressive time series analysis is used to extract reliable features from vibration measurements of civil structures for damage diagnosis. To guarantee the adequacy and applicability of the time series model, Leybourne–McCabe hypothesis test is used. Subsequently, the probability density functions of the autoregressive model parameters and residuals are obtained with the aid of a kernel density estimator. The probability density function sets are considered as damage-sensitive features of the structure and fast distance correlation method is used to make decision for detecting damages in the structure. Experimental data of a well-known three-story laboratory frame and a large-scale bridge benchmark structure are used to verify the efficiency and accuracy of the proposed method. Results indicate the capability of the method to identify the location and severity of damages, even under the simulated operational and environmental variability.

scholarly journals Controlling the Shannon Entropy of Quantum Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Yifan Xing ◽  
Jun Wu
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Shannon Entropy ◽  
Quantum Control ◽  
Control Method ◽  
Controller Design ◽  
Three Dimensional ◽  
Quantum Systems ◽  
Discretization Method

This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking.

scholarly journals Kernel Density Estimation: Theory and Application in Discriminant Analysis

2016 ◽  
Vol 33 (3) ◽  
pp. 267-279 ◽  
Author(s):  
Thomas Ledl
Keyword(s):  
Discriminant Analysis ◽  
Density Function ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Density ◽  
Random Variable ◽  
Kernel Density Estimator ◽  
Density Estimator ◽  
Quadratic Discriminant Analysis ◽  
Bandwidth Parameter

Nowadays, one can find a huge set of methods to estimate the density function of a random variable nonparametrically. Since the first version of the most elementary nonparametric density estimator (the histogram) researchers produced a vast amount of ideas especially corresponding to the issue of choosing the bandwidth parameter in a kernel density estimator model. To focus not only on a descriptive application, the model seems to be quite suitable for application in discriminant analysis, where (multivariate) class densities are the basis for the assignment of a vector to a given class. Thisarticle gives insight to most popular bandwidth parameter selectors as well as to the performance of the kernel density estimator as a classification method compared to the classical linear and quadratic discriminant analysis, respectively. Both a direct estimation in a multivariate space as well as an application of the concept to marginal normalizations of the single variables will be taken into consideration. From this report the gap between theory and application is going to be pointed out.

scholarly journals Complete consistency for recursive probability density estimator of widely orthant dependent samples

2019 ◽  
Vol 39 (1) ◽  
pp. 127-138
Author(s):  
Chenlu Zhuansun ◽  
Xiaoxin Li
Keyword(s):  
Probability Density Function ◽  
Convergence Rate ◽  
Probability Density ◽  
Density Function ◽  
Complete Convergence ◽  
Random Variables ◽  
Density Estimator ◽  
Complete Consistency ◽  
Widely Orthant Dependent ◽  
Dependent Samples

In this paper, we will study the recursive density estimators of the probability density function for widely orthant dependent WOD random variables. The complete consistency and complete convergence rate are established under some general conditions.

Some Properties of Residual R-norm Entropy and Divergence Measures

2017 ◽  
Vol 69 (2) ◽  
pp. 205-221
Author(s):  
M. N. Linu ◽  
S. M. Sunoj
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Present Article ◽  
Shannon Entropy ◽  
Random Variable ◽  
Survival Models ◽  
Divergence Measure ◽  
Conditional Survival ◽  
Reliability Modelling

Shannon entropy plays an important role in measuring the expected uncertainty contained in the probability density function about the predictability of an outcome of a random variable. However, in certain systems, Shannon entropy may not be appropriate, where some generalized versions of it are only suitable. One such generalization is due to Boekee and Lubee [1] , called R-norm entropy. Recently, Nanda and Das [2] studied the R-norm entropy and its divergence measure in the context of used items, useful in reliability modelling. In the present article, we further study R-norm entropy and divergence in the context of weighted models. We also extend these measures to the conditionally specified and conditional survival models, and studied their properties.

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