Law of the iterated logarithm and invariance principle for $M$-estimators
نویسندگان
چکیده
منابع مشابه
An Invariance Principle for the Law of the Iterated Logarithm for Additive Functionals of Markov Chains
In this paper, we prove Strassen’s strong invariance principle for a vector-valued additive functionals of a Markov chain via the martingale argument and the theory of fractional coboundaries. The hypothesis is a moment bound on the resolvent.
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We show that for almost every map in a transversal one-parameter family of piecewise expanding unimodal maps the Birkhoff sum of suitable observables along the forward orbit of the turning point satisfies the law of iterated logarithm. This result will follow from an almost sure invariance principle for the Birkhoff sum, as a function on the parameter space. Furthermore, we obtain a similar res...
متن کاملAn invariance principle for the law of the iterated logarithm for vector-valued additive functionals of Markov chains
In this note, we prove the Strassen’s strong invariance principle for vectorvalued additive functionals of a Markov chain via the martingale argument and the theory of fractional coboundaries. AMS subject classifications: 60F05, 60J05
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 کاملThe law of the iterated logarithm for LNQD sequences
Let [Formula: see text] be a stationary LNQD sequence of random variables with zero means and finite variance. In this paper, by the Kolmogorov type maximal inequality and Stein's method, we establish the result of the law of the iterated logarithm for LNQD sequence with less restriction of moment conditions. We also prove the law of the iterated logarithm for a linear process generated by an L...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1995
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1995-1231036-7