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How to get Central Limit Theorems for global errors of estimates
Applications of Mathematics, Tome 44 (1999) no. 2, pp. 81-96 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 variables, i.e., the context for which they were introduced. This will avoid the mathematical difficulties associated with more complex statistical situations in which these tools have proved to be useful.
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 variables, i.e., the context for which they were introduced. This will avoid the mathematical difficulties associated with more complex statistical situations in which these tools have proved to be useful.
DOI : 10.1023/A:1022240820668
Classification : 60F05, 60F17, 60F25, 62G05, 62G20
Keywords: Central Limit Theorem; global errors; strong approximation; empirical processes; $U$-statistics; Poissonization 
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     title = {How to get {Central} {Limit} {Theorems} for global errors of estimates},
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Berlinet, Alain. How to get Central Limit Theorems for global errors of estimates. Applications of Mathematics, Tome 44 (1999) no. 2, pp. 81-96. doi: 10.1023/A:1022240820668

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