Some statistical properties of the kernel‐diffeomorphism estimator

Saoudi, Samir; Ghorbel, Faouzi; Hillion, A.

doi:10.1002/(sici)1099-0747(199703)13:1<39::aid-asm292>3.0.co;2-j

Cited by 29 publications

(22 citation statements)

References 1 publication

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“…The choice of the optimal smoothing parameter is very critical since it impacts the accuracy of the pdf estimate. In [10], [11], it has been shown that if hN + tends towards 0 when N+ tends towards +∞, the estimatorf b + X,N + (x) is asymptotically unbiased. It has also been shown that if hN + → 0 and N+hN + → +∞ when N+ → +∞, then the MSE of the Kernel estimator tends towards zero.…”

Section: B Output Pdf Estimationmentioning

confidence: 99%

A Novel Non-Parametric Iterative Soft Bit Error Rate Estimation Technique for Digital Communications Systems

Saoudi¹,

Ait-Idir²,

Mochida³

2011

2011 IEEE International Conference on Communications (ICC)

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This paper addresses the problem of unsupervised soft BER estimation for digital communications systems, where no prior knowledge about transmitted information bits is available. We show that the problem of BER estimation is equivalent to estimating the conditional probability density functions (pdf)s of soft channel/receiver outputs. We also propose a non parametric Gaussian Kernel-based pdf estimation technique. Then, we introduce an iterative stochastic expectation maximization (EM) algorithm for the estimation of both a priori and a posteriori probabilities of transmitted information bits, and the classification of soft observations according to transmitted bit values. These inputs serve in the iterative procedure used for the estimation of conditional pdfs. We analyze the performance of the proposed BER estimator and show that is asymptotically unbiased and pointwise consistent. We also provide numerical results in the case of CDMA systems and show that attractive performance is achieved compared with conventional Monte Carlo (MC)-aided techniques.

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Section: B Output Pdf Estimationmentioning

confidence: 99%

A Novel Non-Parametric Iterative Soft Bit Error Rate Estimation Technique for Digital Communications Systems

Saoudi¹,

Ait-Idir²,

Mochida³

2011

2011 IEEE International Conference on Communications (ICC)

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“…The estimation of the probability error for the CDMA communication systems should be mentioned as it will be considered in future work. The generalization to the multivariate case will also be dealt with, in addition to the consideration of densities confined to a bounded support [3,11,12] in order to study the same idea for the diffeomorphism KDE.…”

Section: Discussionmentioning

confidence: 99%

Analytical Plug-In Method for Kernel Density Estimator Applied to Genetic Neutrality Study

Troudi

Alimi

Saoudi

2008

EURASIP J. Adv. Signal Process.

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The plug-in method enables optimization of the bandwidth of the kernel density estimator in order to estimate probability density functions (pdfs). Here, a faster procedure than that of the common plug-in method is proposed. The mean integrated square error (MISE) depends directly upon J(f) which is linked to the second-order derivative of the pdf. As we intend to introduce an analytical approximation of J(f), the pdf is estimated only once, at the end of iterations. These two kinds of algorithm are tested on different random variables having distributions known for their difficult estimation. Finally, they are applied to genetic data in order to provide a better characterisation in the mean of neutrality of Tunisian Berber populations.

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“…This transformation reduces the initial bias around zero bound. Saoudi et al [23] generalized the work of Silverman [15] and proposed the so-called diffeomorphism transformation. The results obtained demonstrate that, in addition to be weak bias near the boundary, the diffeomorphism approach satisfies the statistical properties of Parzen estimator, namely consistency, asymptotic normality and non-biasness.…”

Section: Nonparametric Maintenance Optimization Cost Modelmentioning

confidence: 99%

“…To estimate the reliability function, two kernel estimators are used: the first estimator is based on the diffeomorphism (Log transformation) method (denoted hereafter by Log) [23], and the second estimator is based on JonesSheather plug-in method (denoted hereafter by J-Sh) [22].…”

Section: Nonparametric Maintenance Optimization Cost Modelmentioning

confidence: 99%

Kernel estimator of maintenance optimization model for a stochastically degrading system under different operating environments

Sidibé

Khatab²,

Diallo

et al. 2016

Reliability Engineering & System Safety

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Some statistical properties of the kernel‐diffeomorphism estimator

Cited by 29 publications

References 1 publication

A Novel Non-Parametric Iterative Soft Bit Error Rate Estimation Technique for Digital Communications Systems

A Novel Non-Parametric Iterative Soft Bit Error Rate Estimation Technique for Digital Communications Systems

Analytical Plug-In Method for Kernel Density Estimator Applied to Genetic Neutrality Study

Kernel estimator of maintenance optimization model for a stochastically degrading system under different operating environments

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