Summary
It is shown that the convergence rate of suprema of stationary Gaussian and related processes, such as processes defined by the empirical distribution function, is logarithmically slow, even if the rates are to be uniform over as few as three points. It is proved that the bootstrap approximation provides a substantial improvement.
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Hall, P. On convergence rates of suprema. Probab. Th. Rel. Fields 89, 447–455 (1991). https://doi.org/10.1007/BF01199788
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DOI: https://doi.org/10.1007/BF01199788
Keywords
- Distribution Function
- Stochastic Process
- Probability Theory
- Convergence Rate
- Mathematical Biology