Log-normal approximation of chi-square distributions for signal processing

Jouini, Wassim; Guennec, Daniel Le; Moy, Christophe; Palicot, Jacques

doi:10.1109/ursigass.2011.6050531

Cited by 13 publications

(4 citation statements)

References 2 publications

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“…The estimator of the effect is therefore distributed as a linear combination of variables following the logarithm of a χ 2 distribution. It has been shown that the χ 2 distribution is well approximated by a lognormal distribution (Jouini et al 2011), therefore the distribution of the estimator can be effectively approximated as being normal.…”

Section: Methodsmentioning

confidence: 99%

Meta-analysis of the variance ratio

Traut

2017

Preprint

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IntroductionThe most commonly used effect size when using meta-analysis to compare a measurement of interest in two different populations is the standardised mean difference. This is the mean difference of the measurement divided by the pooled standard deviation in the two groups. The standard deviation is usually supposed to be the same for both groups, although this assumption is often made without any particular evidence. It is possible, however, that the difference of the measurement in the two populations resides precisely in their standard deviations. This could be the case, for example, if a population of patients exhibited more “abnormal” values than a control population – both large and small – even if the mean values were the same. Fisher’s test of equality of variance is designed to compare standard deviations. A variance ratio is a Fisher’s ratio and Fisher distribution can be used to give confidence intervals to the estimate for one study. However, confidence interval for one study can be very wide if the study does not contain enough subjects. Here we present an approach to combine variance ratios of different studies in a meta-analytic way which produces more robust estimates under these circumstances.

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Section: Methodsmentioning

confidence: 99%

Meta-analysis of the variance ratio

Traut

2017

Preprint

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“…Here, we adopt the Log-Normal distribution to approximate the chi-square distribution in (26) and (27). This approximation is based on the observation that the probability density function of the chi-square distribution is nearly identical to that of the Log-Normal distribution when the degree of freedom of the chi-square distribution is large [2], [47]. Thus, we obtain T ∼ F 1 LogN (µ F , σ 2 F ) + P 1 LogN (µ P , σ 2 P ), where…”

Section: B Optimal Thresholdmentioning

confidence: 99%

Physical Layer Authentication Based on Channel Polarization Response in Dual-Polarized Antenna Communication Systems

Dong

Guo

et al. 2023

IEEE Trans.Inform.Forensic Secur.

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This study presents a novel approach for physical layer authentication based on channel polarization response (CPR). CPR is sensitive to variation in the physical properties of scatterers, and the CPR difference between various channels is higher than the channel frequency response (CFR) under rich scattering scenarios. Additionally, the estimation of CPR is continuous, the authentication interval can be adjusted according to the channel coherence time, then the proposed scheme can be applied to any rich scattering scenarios, including highly dynamic scenarios. Since the received polarization state is fixed during the channel coherence time, we can coherently stack the received polarization state to improve the signal to noise ratio (SNR) and the estimation accuracy of CPR, thereby achieving high authentication accuracy under ultra-low SNR. Moreover, since the transmitted polarization state of various transmitters is different, because of their unique hardware deficiencies, and since the CPR is dependent on the transmitted polarization state, the CPR of other transmitters is different, allowing the resolution of co-located attacks. We theoretically drive the false alarm probability, detection probability, optimal discriminant threshold, computational complexity, optimal stacking numbers, and optimal CPR points for authentication. Furthermore, extensive simulations and experiments are performed to verify the validity and effectiveness of the proposed scheme.

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“…The distributional assumption Y $ N ð0; s 2 IÞ implies that ðY i 2Y j Þ 2 follows a x 2 -distribution x 2 ð2Þ for i 6 ¼ j: This yields relatively complex distributions for the random effect vector u 2 R nðn21Þ=2 and the logarithmic residual vector logðeÞ 2 R nðn21Þ=2 . However, it is shown that log-normal distributions offer appropriate approximations for x 2 -distributions (Jouini et al 2011). The dependent pseudovariables logððY i 2Y j Þ 22 Þ ¼2 logððY i 2Y j Þ 2 Þ can be therefore treated approximately as normally distributed random variables, and, thus, it is adequate to assume that, for a known expression, covariance matrix G u…”

Section: Dimension Reduction-estimation Of Inverse Bandwidth Parametersmentioning

confidence: 99%

Scalable Nonparametric Prescreening Method for Searching Higher-Order Genetic Interactions Underlying Quantitative Traits

Kontio

Sillanpää

2019

Genetics

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Gaussian process (GP)-based automatic relevance determination (ARD) is known to be an efficient technique for identifying determinants of gene-by-gene interactions important to trait variation. However, the estimation of GP models is feasible only for low-dimensional datasets (∼200 variables), which severely limits application of the GP-based ARD method for high-throughput sequencing data. In this paper, we provide a nonparametric prescreening method that preserves virtually all the major benefits of the GP-based ARD method and extends its scalability to the typical high-dimensional datasets used in practice. In several simulated test scenarios, the proposed method compared favorably with existing nonparametric dimension reduction/prescreening methods suitable for higher-order interaction searches. As a real-data example, the proposed method was applied to a high-throughput dataset downloaded from the cancer genome atlas (TCGA) with measured expression levels of 16,976 genes (after preprocessing) from patients diagnosed with acute myeloid leukemia.

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Log-normal approximation of chi-square distributions for signal processing

Cited by 13 publications

References 2 publications

Meta-analysis of the variance ratio

Meta-analysis of the variance ratio

Physical Layer Authentication Based on Channel Polarization Response in Dual-Polarized Antenna Communication Systems

Scalable Nonparametric Prescreening Method for Searching Higher-Order Genetic Interactions Underlying Quantitative Traits

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