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Physical Sciences and Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

1996

Mathematics

Research Scholars in Residence

Articles 1 - 3 of 3

Full-Text Articles in Physical Sciences and Mathematics

A Note On Distributions Of True Versus Fabricated Data, Theodore P. Hill Dec 1996

A Note On Distributions Of True Versus Fabricated Data, Theodore P. Hill

Research Scholars in Residence

New empirical evidence and statistical derivations of Benford’s Law have led to successful goodness-of fit tests to detect fraud in accounting data. Several recent case studies support the hypothesis that fabricated data does not conform to expected true digital frequencies.

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Strongly-Consistent, Distribution-Free Confidence Intervals For Quantiles, David Gilat, Theodore P. Hill Aug 1996

Strongly-Consistent, Distribution-Free Confidence Intervals For Quantiles, David Gilat, Theodore P. Hill

Research Scholars in Residence

Strongly-consistent, distribution-free confidence intervals are derived to estimate the fixed quantiles of an arbitrary unknown distribution, based on order statistics of an iid sequence from that distribution. This new method, unlike classical estimates, works for totally arbitrary (including discontinuous) distributions, and is based on recent one-sided strong laws of large numbers.

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Strong Laws For L- And U-Statistics, J. Aaronson, R. Burton, H. Dehling, D. Gilat, Theodore P. Hill, B. Weiss Jul 1996

Strong Laws For L- And U-Statistics, J. Aaronson, R. Burton, H. Dehling, D. Gilat, Theodore P. Hill, B. Weiss

Research Scholars in Residence

Strong laws of large numbers are given for L-statistics (linear combinations of order statistics) and for U-statistics (averages of kernels of random samples) for ergodic stationary processes, extending classical theorems of Hoeffding and of Helmers for iid sequences. Examples are given to show that strong and even weak convergence may fail if the given sufficient conditions are not satisfied, and an application is given to estimation of correlation dimension of invariant measures.

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