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Distribution/correlation-free test for two-sample means in high-dimensional functional data with eigenvalue decay relaxed
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作者 Kaijie Xue 《Science China Mathematics》 SCIE CSCD 2023年第10期2337-2346,共10页
We propose a methodology for testing two-sample means in high-dimensional functional data that requires no decaying pattern on eigenvalues of the functional data.To the best of our knowledge,we are the first to consid... We propose a methodology for testing two-sample means in high-dimensional functional data that requires no decaying pattern on eigenvalues of the functional data.To the best of our knowledge,we are the first to consider and address such a problem.To be specific,we devise a confidence region for the mean curve difference between two samples,which directly establishes a rigorous inferential procedure based on the multiplier bootstrap.In addition,the proposed test permits the functional observations in each sample to have mutually different distributions and arbitrary correlation structures,which is regarded as the desired property of distribution/correlation-free,leading to a more challenging scenario for theoretical development.Other desired properties include the allowance for highly unequal sample sizes,exponentially growing data dimension in sample sizes and consistent power behavior under fairly general alternatives.The proposed test is shown uniformly convergent to the prescribed significance,and its finite sample performance is evaluated via the simulation study and an application to electroencephalography data. 展开更多
关键词 high dimension functional data eigenvalue decay relaxed multiplier bootstrap distribution/correlation-free
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Brittleness index predictions from Lower Barnett Shale well-log data applying an optimized data matching algorithm at various sampling densities 被引量:1
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作者 David A.Wood 《Geoscience Frontiers》 SCIE CAS CSCD 2021年第6期444-457,共14页
The capability of accurately predicting mineralogical brittleness index (BI) from basic suites of well logs is desirable as it provides a useful indicator of the fracability of tight formations.Measuring mineralogical... The capability of accurately predicting mineralogical brittleness index (BI) from basic suites of well logs is desirable as it provides a useful indicator of the fracability of tight formations.Measuring mineralogical components in rocks is expensive and time consuming.However,the basic well log curves are not well correlated with BI so correlation-based,machine-learning methods are not able to derive highly accurate BI predictions using such data.A correlation-free,optimized data-matching algorithm is configured to predict BI on a supervised basis from well log and core data available from two published wells in the Lower Barnett Shale Formation (Texas).This transparent open box (TOB) algorithm matches data records by calculating the sum of squared errors between their variables and selecting the best matches as those with the minimum squared errors.It then applies optimizers to adjust weights applied to individual variable errors to minimize the root mean square error (RMSE)between calculated and predicted (BI).The prediction accuracy achieved by TOB using just five well logs (Gr,ρb,Ns,Rs,Dt) to predict BI is dependent on the density of data records sampled.At a sampling density of about one sample per 0.5 ft BI is predicted with RMSE~0.056 and R^(2)~0.790.At a sampling density of about one sample per0.1 ft BI is predicted with RMSE~0.008 and R^(2)~0.995.Adding a stratigraphic height index as an additional (sixth)input variable method improves BI prediction accuracy to RMSE~0.003 and R^(2)~0.999 for the two wells with only 1 record in 10,000 yielding a BI prediction error of>±0.1.The model has the potential to be applied in an unsupervised basis to predict BI from basic well log data in surrounding wells lacking mineralogical measurements but with similar lithofacies and burial histories.The method could also be extended to predict elastic rock properties in and seismic attributes from wells and seismic data to improve the precision of brittleness index and fracability mapping spatially. 展开更多
关键词 Well-log brittleness index estimates Data record sample densities Zoomed-in data interpolation correlation-free prediction analysis Mineralogical and elastic influences
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