Abstract
AbstractLet X1,X2,…,X n be a sequence of independent random variables with zero means and finite variances. In Sect. 2.1.3, we have described Cramér's moderate deviation results for \(\left( {\sum\nolimits_{i = 1}^n {X_i } } \right)/\left( {\sum\nolimits_{i = 1}^n {EX_i^2 } } \right)^{1/2}\) . In this chapter we show that similar to self-normalized large and moderate deviation theorems in Chaps. 3 and 6, Cramér-type moderate deviation results again hold for self-normalized sums under minimal moment conditions.KeywordsModerate DeviationIndependent Random VariableAbsolute ConstantIterate LogarithmLengthy CalculationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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