The law of the iterated logarithm for LNQD sequences [PDF]
Journal of Inequalities and Applications, 2018 Let { ξ i , i ∈ Z } $\{\xi_{i},i\in{\mathbb{Z}}\}$ 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 ...
Yong Zhang
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The Law of the Iterated Logarithm for Linear Processes Generated by a Sequence of Stationary Independent Random Variables under the Sub-Linear Expectation [PDF]
Entropy, 2021 In this paper, we obtain the law of iterated logarithm for linear processes in sub-linear expectation space. It is established for strictly stationary independent random variable sequences with finite second-order moments in the sense of non-additive ...
Wei Liu, Yong Zhang
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On the law of the iterated logarithm. [PDF]
Proc Natl Acad Sci U S A, 1969 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.
Slivka J.
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A law of the iterated logarithm for Grenander's estimator. [PDF]
Stoch Process Their Appl, 2016 In this note we prove the following law of the iterated logarithm for the Grenander estimator of a monotone decreasing density: If $f(t_0) > 0$, $f'(t_0) < 0$, and $f'$ is continuous in a neighborhood of $t_0$, then \begin{eqnarray*} \limsup_{n\rightarrow \infty} \left ( \frac{n}{2\log \log n} \right )^{1/3} ( \widehat{f}_n (t_0 ) - f(t_0 ...
Dümbgen L, Wellner JA, Wolff M.
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On the Law of the Iterated Logarithm
Annals of Probability, 1974 A triumvirate of sufficient conditions is given for unbounded, independent random variables to obey the Law of the Iterated Logarithm (LIL). As special cases, new results for weighted i.i.d. random variables and the Hartman-Wintner theorem are obtained.
Henry Teicher
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Self-Normalized Moderate Deviations for Degenerate U-Statistics [PDF]
EntropyIn this paper, we study self-normalized moderate deviations for degenerate U-statistics of order 2. Let {Xi,i≥1} be i.i.d. random variables and consider symmetric and degenerate kernel functions in the form h(x,y)=∑l=1∞λlgl(x)gl(y), where λl>0, Egl(X1)=0,
Lin Ge, Hailin Sang, Qi-Man Shao
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Sharp Second-Order Pointwise Asymptotics for Lossless Compression with Side Information [PDF]
Entropy, 2020 The problem of determining the best achievable performance of arbitrary lossless compression algorithms is examined, when correlated side information is available at both the encoder and decoder.
Lampros Gavalakis, Ioannis Kontoyiannis
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A law of iterated logarithm for the subfractional Brownian motion and an application [PDF]
Journal of Inequalities and Applications, 2018 Let SH={StH,t≥0} $S^{H}=\{S^{H}_{t},t\geq0\}$ be a sub-fractional Brownian motion with Hurst index 00) $(x>0)$ with ΦH(0)=0 $\Phi_{H}(0)=0$.
Hongsheng Qi, Litan Yan
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Laws of the iterated logarithm for nonparametric sequential density estimators [PDF]
Journal of Statistical Theory and Applications (JSTA), 2013 In this note, we establish a law of iterated logarithm for a triangular array of a random number of independent random variables and apply it to obtain laws of iterated logarithm for the sequential nonparametric density estimators.
Karima Lagha, Smail Adjabi
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The law of iterated logarithm for combinatorial multisets
Lietuvos Matematikos Rinkinys, 2005 There is no abstract.
Jolita Norkūnienė
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