ITERATED LOGARITHM INEQUALITIES
نویسندگان
چکیده
منابع مشابه
Self-normalized Processes: Exponential Inequalities, Moment Bounds and Iterated Logarithm Laws by Victor
Self-normalized processes arise naturally in statistical applications. Being unit free, they are not affected by scale changes. Moreover, selfnormalization often eliminates or weakens moment assumptions. In this paper we present several exponential and moment inequalities, particularly those related to laws of the iterated logarithm, for self-normalized random variables including martingales. T...
متن کاملSelf - Normalized Processes : Exponential Inequalities , Moment Bounds and Iterated Logarithm Laws
Self-normalized processes arise naturally in statistical applications. Being unit free, they are not affected by scale changes. Moreover, self-normalization often eliminates or weakens moment assumptions. In this paper we present several exponential and moment inequalities, particularly those related to laws of the iterated logarithm, for self-normalized random variables including martingales. ...
متن کاملOn the law of the iterated logarithm.
The law of the iterated logarithm provides a family of bounds all of the same order such that with probability one only finitely many partial sums of a sequence of independent and identically distributed random variables exceed some members of the family, while for others infinitely many do so. In the former case, the total number of such excesses has therefore a proper probability distribution...
متن کاملSelf-normalized laws of the iterated logarithm
Stronger versions of laws of the iterated logarithm for self-normalized sums of i.i.d. random variables are proved.
متن کاملIterated Laguerre and Turán Inequalities
New inequalities are investigated for real entire functions in the Laguerre-Pólya class. These are generalizations of the classical Turán and Laguerre inequalities. They provide necessary conditions for certain real entire functions to have only real zeros.
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1967
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.57.5.1188