Results 1 to 10 of about 16,691 (298)

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.
europepmc   +8 more sources

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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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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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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The Other Law of the Iterated Logarithm [PDF]

The Annals of Probability, 1975
Let $\{X_n\}$ be a sequence of independent, identically distributed random variables with $EX_1 = 0, EX_1^2 = 1$. Define $S_n = X_1 + \cdots + X_n$, and $A_n = \max_{1\leqq k\leqq n} |S_k|$. We prove that $\lim \inf A_n(n/\log \log n)^{-\frac{1}{2}} = \pi/8^{\frac{1}{2}}$ with probability one.
Naresh C. Jain, William E. Pruitt
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Self-Normalized Moderate Deviations for Degenerate U-Statistics [PDF]

Entropy
In 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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An analogue of the law of the iterated logarithm [PDF]

Proceedings of the American Mathematical Society, 1955
Glen Baxter
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On the Law of the Iterated Logarithm. II

Indagationes Mathematicae (Proceedings), 1964
Olaf P. Stackelberg
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