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Using Pearson’s System of Curves to Approximate the Distributions of the Difference between Two Correlated Estimates of Signal-to-Noise Ratios: The Cases of Bivariate Normal and Bivariate Lognormal Distributions

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Open Journal of Statistics 2024年第3期14卷 207-227页

作者： Mohamed M. Shoukri Department of Epidemiology and Biostatistics Schulich School of Medicine and Dentistry University of Western Ontario London Ontario Canada

Background: The signal-to-noise ratio (SNR) is recognized as an index of measurements reproducibility. We derive the maximum likelihood estimators of SNR and discuss confidence interval construction on the difference between two correlated SNRs when the readings are from bivariate normal and bivariate lognormal distribution. We use the Pearsons system of curves to approximate the difference between the two estimates and use the bootstrap methods to validate the approximate distributions of the statistic of interest. methods: The paper uses the delta method to find the first four central moments, and hence the skewness and kurtosis which are important in the determination of the parameters of the Pearsons distribution. Results: The approach is illustrated in two examples;one from veterinary microbiology and food safety data and the other on data from clinical medicine. We derived the four central moments of the target statistics, together with the bootstrap method to evaluate the parameters of Pearsons distribution. The fitted Pearsons curves of Types I and II were recommended based on the available data. The R-codes are also provided to be readily used by the readers.

关键词： Signal-to-Noise Ratio Bivariate Distributions bootstrap methods Delta Method Pearson System of Curves

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Thermomechanical analysis of long-term global modal and local deformation measurements of the Kishwaukee Bridge using the bootstrap

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Earthquake Engineering and Engineering Vibration 2004年第1期3卷 107-115页

作者： George M.Lloyd Ming L.Wang Department of Civil and Material Engineering University of Illinois at Chicago

In this paper we present a comparative analysis of global frequency and local deformation data for a large concrete bridge. The asymptotic probability distributions of the central statistics are presented, and compared with empirical bootstrap estimates. bootstrapped distributions are calculated from reference data obtained during 1999–2000 and used to develop change-point alarm criteria for the structure, using reasonable sensitivity measures developed from FEM simulations and structural analysis. The implications of the frequency data are discussed in conjunction with the strain and displacement measurements in order to discern if the load carrying capacity of the bridge has been affected. The critical need for more advanced temperature compensation models for large structures continually in thermal disequilibrium is discussed.

关键词： thermomechanical effects bootstrap methods local & global monitoring long term measurement concrete bridge

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Bias and Mean Square Error of Reliability Estimators under the One and Two Random Effects Models: The Effect of Non-Normality

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Open Journal of Statistics 2016年第2期6卷 254-273页

作者： Mohamed M. Shoukri Tusneem Al-Hassan Michael DeNiro Abdelmoneim El Dali Futwan Al-Mohanna Department of Cell Biology King Faisal Specialist Hospital and Research Center Riyadh Saudi Arabia Al-Faisal University College of Medicine Riyadh Saudi Arabia The Oncology Center King Faisal Specialist Hospital and Research Center Riyadh Saudi Arabia Department of Biostatistics Epidemiology and Scientific Computing King Faisal Specialist Hospital and Research Center Riyadh Saudi Arabia

The coefficient of reliability is often estimated from a sample that includes few subjects. It is therefore expected that the precision of this estimate would be low. Measures of precision such as bias and variance depend heavily on the assumption of normality, which may not be tenable in practice. Expressions for the bias and variance of the reliability coefficient in the one and two way random effects models using the multivariate Taylor’s expansion have been obtained under the assumption of normality of the score (Atenafu et al. [1]). In the present paper we derive analytic expressions for the bias and variance, hence the mean square error when the measured responses are not normal under the one-way data layout. Similar expressions are derived in the case of the two-way data layout. We assess the effect of departure from normality on the sample size requirements and on the power of Wald’s test on specified hypotheses. We analyze two data sets, and draw comparisons with results obtained via the bootstrap methods. It was found that the estimated bias and variance based on the bootstrap method are quite close to those obtained by the first order approximation using the Taylor’s expansion. This is an indication that for the given data sets the approximations are quite adequate.

关键词： Rater’s Reliability Random Effects Models Multivariate Taylor’s Expansion Wald’s Confidence Interval bootstrap methods

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