scholarly journals Blind Frequency Estimation and Symbol Recovery for the Analytically Solvable Chaotic System

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 791
Author(s):  
Ang Zhou ◽  
Shilian Wang ◽  
Junshan Luo
Keyword(s):  
Maximum Likelihood ◽  
Lower Bound ◽  
Maximum Likelihood Estimator ◽  
Chaotic System ◽  
Frequency Estimation ◽  
Frequency Parameter ◽  
Error Performance ◽  
Likelihood Estimator ◽  
Chaos Communication ◽  
Symbol Detection

The analytically solvable chaotic system (ASCS) is a promising chaotic system in chaos communication and radar fields. In this paper, we propose a maximum likelihood estimator (MLE) to estimate the frequency of ASCS, then a difference-integral (DI) detector is designed with the estimated frequency, and the symbols encoded in the signal are recovered. In the proposed method, the frequency parameter is estimated by an MLE based on the square power of the received signal. The Cramer-Rao lower bound in blind frequency estimation and the bit error performance in symbol detection are analyzed to assess the performance of the proposed method. Numerical results validate the analysis and demonstrate that the proposed symbol detector achieves the error performance with a little cost of 1 dB compared to the coherent detector. The robustness of the proposed method towards parameters is also verified through simulations.

scholarly journals A note on Hammersley's inequality for estimating the normal integer mean

2003 ◽  
Vol 2003 (34) ◽  
pp. 2147-2156 ◽  
Author(s):  
Rasul A. Khan
Keyword(s):  
Maximum Likelihood ◽  
Lower Bound ◽  
Maximum Likelihood Estimator ◽  
Random Sample ◽  
Unbiased Estimator ◽  
Minimum Variance ◽  
Likelihood Estimator ◽  
Sample Mean ◽  
Bhattacharyya Bounds ◽  
Limiting Property

LetX1,X2,…,Xnbe a random sample from a normalN(θ,σ2)distribution with an unknown meanθ=0,±1,±2,…. Hammersley (1950) proposed the maximum likelihood estimator (MLE)d=[X¯n], nearest integer to the sample mean, as an unbiased estimator ofθand extended the Cramér-Rao inequality. The Hammersley lower bound for the variance of any unbiased estimator ofθis significantly improved, and the asymptotic (asn→∞) limit of Fraser-Guttman-Bhattacharyya bounds is also determined. A limiting property of a suitable distance is used to give some plausible explanations why such bounds cannot be attained. An almost uniformly minimum variance unbiased (UMVU) like property ofdis exhibited.

The Comparison Between the Bayes Estimator and the Maximum Likelihood Estimator of the Reliability Function for Negative Exponential Distribution

2018 ◽  
pp. 439
Author(s):  
Hazim Mansour Gorgees ◽  
Bushra Abdualrasool Ali ◽  
Raghad Ibrahim Kathum
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Exponential Distribution ◽  
Reliability Function ◽  
Bayes Estimator ◽  
Likelihood Estimator ◽  
Monte Carlo Simulation Technique ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Better Than

     In this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.

scholarly journals Transforming variables to central normality

2021 ◽  
Author(s):  
Jakob Raymaekers ◽  
Peter J. Rousseeuw
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Real Data ◽  
Data Sets ◽  
Transformation Parameter ◽  
Likelihood Estimator ◽  
Extensive Simulation ◽  
Highly Sensitive

AbstractMany real data sets contain numerical features (variables) whose distribution is far from normal (Gaussian). Instead, their distribution is often skewed. In order to handle such data it is customary to preprocess the variables to make them more normal. The Box–Cox and Yeo–Johnson transformations are well-known tools for this. However, the standard maximum likelihood estimator of their transformation parameter is highly sensitive to outliers, and will often try to move outliers inward at the expense of the normality of the central part of the data. We propose a modification of these transformations as well as an estimator of the transformation parameter that is robust to outliers, so the transformed data can be approximately normal in the center and a few outliers may deviate from it. It compares favorably to existing techniques in an extensive simulation study and on real data.

Covariance matrix of the bias-corrected maximum likelihood estimator in generalized linear models

2013 ◽  
Vol 55 (3) ◽  
pp. 643-652
Author(s):  
Gauss M. Cordeiro ◽  
Denise A. Botter ◽  
Alexsandro B. Cavalcanti ◽  
Lúcia P. Barroso
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Covariance Matrix ◽  
Generalized Linear Models ◽  
Linear Models ◽  
Likelihood Estimator

Large deviations and Berry–Esseen inequalities for estimators in nonhomogeneous diffusion driven by fractional Brownian motion

2020 ◽  
Vol 28 (3) ◽  
pp. 183-196
Author(s):  
Kouacou Tanoh ◽  
Modeste N’zi ◽  
Armel Fabrice Yodé
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Maximum Likelihood ◽  
Large Deviations ◽  
Stochastic Differential Equation ◽  
Fractional Brownian Motion ◽  
Maximum Likelihood Estimator ◽  
Bayes Estimator ◽  
Likelihood Estimator

AbstractWe are interested in bounds on the large deviations probability and Berry–Esseen type inequalities for maximum likelihood estimator and Bayes estimator of the parameter appearing linearly in the drift of nonhomogeneous stochastic differential equation driven by fractional Brownian motion.

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