SIAM Journal on Optimization
Bootstrap of deviation probabilities with applications
Journal of Multivariate Analysis
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We prove general theorems that characterize situations in which we could have asymptotic closeness between the original statistics H"n and its bootstrap version H"n^*, without stipulating the existence of weak limits. As one possible application we introduce a novel goodness of fit test based on the modification of Total Variation metric. This new statistic is more sensitive than the Kolmogorov-Smirnov statistic, it applies to higher dimensions, and it does not converge weakly; but we show that it can be bootstrapped.