How to get Central Limit Theorems for global errors of estimates

Alain Berlinet

Applications of Mathematics (1999)

  • Volume: 44, Issue: 2, page 81-96
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Berlinet, Alain. "How to get Central Limit Theorems for global errors of estimates." Applications of Mathematics 44.2 (1999): 81-96. <http://eudml.org/doc/33028>.

@article{Berlinet1999,
abstract = {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.},
author = {Berlinet, Alain},
journal = {Applications of Mathematics},
keywords = {Central Limit Theorem; global errors; strong approximation; empirical processes; $U$-statistics; Poissonization; limit theorems; Poissonization; global errors; strong approximation; empirical processes; U-statistics},
language = {eng},
number = {2},
pages = {81-96},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {How to get Central Limit Theorems for global errors of estimates},
url = {http://eudml.org/doc/33028},
volume = {44},
year = {1999},
}

TY - JOUR
AU - Berlinet, Alain
TI - How to get Central Limit Theorems for global errors of estimates
JO - Applications of Mathematics
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 44
IS - 2
SP - 81
EP - 96
AB - 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.
LA - eng
KW - Central Limit Theorem; global errors; strong approximation; empirical processes; $U$-statistics; Poissonization; limit theorems; Poissonization; global errors; strong approximation; empirical processes; U-statistics
UR - http://eudml.org/doc/33028
ER -

References

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