U-statistics for estimating performance metrics in forensic handwriting analysis

A class of computationally efficient approximations to a set of natural U-statistics and related U-processes that arise in forensic and biometric comparisons have been developed. This paper details the asymptotic characterization of the natural U-statistics, the development of computationally efficient approximations and expected error bounds of said approximations. The developed statistical methods are presented in the context of forensic handwriting comparisons and are used to estimate the rate at which the random match probability (RMP) decreases as a function of the amount of writing available in the comparison samples. Although presented in a forensic handwriting comparison context, similar problems arise in machine learning or pattern recognition where the task is to classify a batch of exchangeable objects that arise from the same class. Similarly, the developed methods can be used to estimate the rate at which the error rate decreases as the number of objects to be classified increases.

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