Robustness of the sample correlation - the bivariate lognormal case

Lai, C. D.; Rayner, J. C. W.; Hutchinson, T. P.

doi:10.1155/s1173912699000012

Cited by 22 publications

(17 citation statements)

References 3 publications

(4 reference statements)

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“…The second part of Table 1 lists ASV of all correlations under the lognormal distribution with σ = and σ = . In this case, the Pearson correlation has extremely large asymptotic variances, the result agreeing well with [19,23]. The asymptotic variance ofrp involves the fourth moment and is given by Witting and Müller-Funk ( [40]) as follows.…”

Section: Asymptotic Relative E Ciencysupporting

confidence: 53%

Two symmetric and computationally efficient Gini correlations

Vanderford

Sang

Dang

2020

Dependence Modeling

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Standard Gini correlation plays an important role in measuring the dependence between random variables with heavy-tailed distributions. It is based on the covariance between one variable and the rank of the other. Hence for each pair of random variables, there are two Gini correlations and they are not equal in general, which brings a substantial difficulty in interpretation. Recently, Sang et al (2016) proposed a symmetric Gini correlation based on the joint spatial rank function with a computation cost of O(n2) where n is the sample size. In this paper, we study two symmetric and computationally efficient Gini correlations with the computational complexity of O(n log n). The properties of the new symmetric Gini correlations are explored. The influence function approach is utilized to study the robustness and the asymptotic behavior of these correlations. The asymptotic relative efficiencies are considered to compare several popular correlations under symmetric distributions with different tail-heaviness as well as an asymmetric log-normal distribution. Simulation and real data application are conducted to demonstrate the desirable performance of the two new symmetric Gini correlations.

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Section: Asymptotic Relative E Ciencysupporting

confidence: 53%

Two symmetric and computationally efficient Gini correlations

Vanderford

Sang

Dang

2020

Dependence Modeling

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“…Numerous authors reviewed by Johnson et al (1995) and Lai et al (1999) have derived expressions for the first four moments of r in terms of the cumulants and cross-cumulants of the parent non-normal population. Despite this attention given to r, the magnitude of the bias and the variance of r are still relatively poorly understood for general bivariate nonnormal populations.…”

Section: Performance Of R 2 and R Under Bivariate Normalitymentioning

confidence: 99%

Improved estimators of correlation and R² for skewed hydrologic data

Barber

Lamontagne

Vogel

2019

Hydrological Sciences Journal

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The coefficient of determination R 2 and Pearson correlation coefficient ρ = R are standard metrics in hydrology for the evaluation of the goodness of fit between model simulations and observations, and as measures of the degree of dependence of one variable upon another. We show that the standard product moment estimator of ρ, termed r, while well-behaved for bivariate normal data, is upward biased and highly variable for bivariate non-normal data. We introduce three alternative estimators of ρ which are nearly unbiased and exhibit much less variability than r for non-normal data. We also document remarkable upward bias and tremendous increases in variability associated with r using both synthetic data and daily streamflow simulations from 905 calibrated rainfall-runoff models. We show that estimators of ρ = R accounting for skewness are needed for daily streamflow series because they exhibit high variability and skewness compared to, for example, monthly/annual series, where r should perform well.

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“…Although the correlation coefficient is commonly used to characterize the complicated rainfall spatial structure, accuracy and reliability associated with its estimation are not completely resolved (Stedinger 1981;Shimizu 1993;Lai et al 1999;Ciach and Krajewski 2006). The correlation using traditional Pearson formula can be overestimated in some cases for which rain rates follow non-normal distributions (Kowalski 1972).…”

Section: B Correlation Structurementioning

confidence: 99%

Evaluation of TRMM Ground-Validation Radar-Rain Errors Using Rain Gauge Measurements

Wang

Wolff

2010

Journal of Applied Meteorology and Climatology

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Ground-validation (GV) radar-rain products are often utilized for validation of the Tropical Rainfall Measuring Mission (TRMM) spaced-based rain estimates, and hence, quantitative evaluation of the GV radar-rain product error characteristics is vital. This study uses quality-controlled gauge data to compare with TRMM GV radar rain rates in an effort to provide such error characteristics. The results show that significant differences of concurrent radar-gauge rain rates exist at various time scales ranging from 5 min to 1 day, despite lower overall long-term bias. However, the differences between the radar area-averaged rain rates and gauge point rain rates cannot be explained as due to radar error only. The error variance separation method is adapted to partition the variance of radar-gauge differences into the gauge area-point error variance and radar rain estimation error variance. The results provide relatively reliable quantitative uncertainty evaluation of TRMM GV radar rain estimates at various times scales, and are helpful to better understand the differences between measured radar and gauge rain rates.It is envisaged that this study will contribute to better utilization of GV radar rain products to validate versatile spaced-based rain estimates from TRMM, as well as the proposed Global Precipitation Measurement, and other satellites.

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Robustness of the sample correlation - the bivariate lognormal case

Cited by 22 publications

References 3 publications

Two symmetric and computationally efficient Gini correlations

Two symmetric and computationally efficient Gini correlations

Improved estimators of correlation and R² for skewed hydrologic data

Evaluation of TRMM Ground-Validation Radar-Rain Errors Using Rain Gauge Measurements

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Robustness of the sample correlation - the bivariate lognormal case

Cited by 22 publications

References 3 publications

Two symmetric and computationally efficient Gini correlations

Two symmetric and computationally efficient Gini correlations

Improved estimators of correlation and R2 for skewed hydrologic data

Evaluation of TRMM Ground-Validation Radar-Rain Errors Using Rain Gauge Measurements

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Product

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Improved estimators of correlation and R² for skewed hydrologic data