The integral limit theorem in the first passage problem for sums of independent nonnegative lattice variables.
Virchenko, Yuri P., Yastrubenko, M.I. (2006)
Abstract and Applied Analysis
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The integral limit theorem in the first passage problem for sums of independent nonnegative lattice variables.
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The asymptotic behavior of global errors of functional estimates plays a key role in hypothesis testing and confidence interval building. Whereas for pointwise errors asymptotic normality often easily follows from standard Central Limit Theorems, global errors asymptotics involve some additional techniques such as strong approximation, martingale theory and Poissonization. We review these techniques in the framework of density estimation from independent identically distributed random...
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