Abstract
Motivated by asymptotic expansions in the central limit theorem, we find exact norms of a sequence of Stein-type operators. The proof is based on new stochastic comparisons in distribution between the difference of two independent transformed normal variables and the standard normal distribution.
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Mathematics Subject Classifications (2000): 60F05; 60E15
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Lefèvre, C., Utev, S. Exact norms of a Stein-type operator and associated stochastic orderings. Probab. Theory Relat. Fields 127, 353–366 (2003). https://doi.org/10.1007/s00440-003-0288-9
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DOI: https://doi.org/10.1007/s00440-003-0288-9
Keywords or phrases:
- Stein-type operator
- Exact norms
- Central limit theorem
- Stochastic order in distribution