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A law of the iterated logarithm for error density estimator in censored linear regression
Journal of nonparametric statistics (Print), 2022We consider the strong consistency of the nonparametric estimation of error density in linear regression with right censored data. The estimator is defined to be the kernel-smoothed estimator of error density, which makes use of the Kaplan-Meier ...
Fuxia Cheng
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Lower deviations in β-ensembles and law of iterated logarithm in last passage percolation
Israel Journal of Mathematics, 2019For last passage percolation (LPP) on ℤ2 with exponential passage times, let Tn denote the passage time from (1, 1) to (n,n). We investigate the law of iterated logarithm of the sequence {Tn}n≥1; we show that liminfn→∞Tn−4nn1/3(loglogn)1/3\documentclass ...
Riddhipratim Basu +3 more
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Illinois Journal of Mathematics
This paper investigates whether two independent Elephant Random Walks (ERWs) on $\mathbb{Z}$, each with a different memory parameter, can meet infinitely often, extending the work of Roy, Takei, and Tanemura.
Shuhei Shibata, Tomoyuki Shirai
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This paper investigates whether two independent Elephant Random Walks (ERWs) on $\mathbb{Z}$, each with a different memory parameter, can meet infinitely often, extending the work of Roy, Takei, and Tanemura.
Shuhei Shibata, Tomoyuki Shirai
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Memoirs of the American Mathematical Society
Let Y Y be a symmetric ...
Michael Marcus, Jay Rosen
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Let Y Y be a symmetric ...
Michael Marcus, Jay Rosen
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Law of the iterated logarithm for error density estimators in nonlinear autoregressive models
Communications in Statistics - Theory and Methods, 2020In this paper, we consider the law of the iterated logarithm for error density estimators in the nonlinear autoregressive models under appropriate assumptions.
Tianze Liu, Yong Zhang
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1994
Let the kernel Φ have the rank r = 1 and satisfy the conditions $$Eg_1^2 < \infty ,E|\Phi {|^{4/3}} < \infty $$ (9.1.1)
V. S. Koroljuk, Yu. V. Borovskich
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Let the kernel Φ have the rank r = 1 and satisfy the conditions $$Eg_1^2 < \infty ,E|\Phi {|^{4/3}} < \infty $$ (9.1.1)
V. S. Koroljuk, Yu. V. Borovskich
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On the law of the iterated logarithm. I
Indagationes Mathematicae (Proceedings), 1955Die Verff. beweisen den folgenden Satz: Es sei \(n_1 < n_2 < \cdots\) eine unendliche Folge von positiven Zahlen mit \(n_{\nu+1}/n_\nu \geq q>1 \; (\nu =1,2,...)\). Für fast alle reellen \(x\) ist dann \(\limsup_{N \to \infty} (N \log\log N )^{-1/2} \left|\sum_{\nu=1}^N \exp 2 \pi i n_\nu x \right| =1\).
Erdős, Pál, Gál, István Sándor
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A new law of iterated logarithm
Acta Mathematica Hungarica, 1990The authors study the limit behaviour as \(t\to \infty\) of the process \[ \xi(t)=\sup \{s :\;e\leq s\leq t,\quad W(s)\geq (2s \log \log s)^{1/2}\}, \] where \(W(t)\) is a Wiener process. The main result is the following Theorem: \[ \liminf_{t\to \infty}[\frac{\log \log t)^{1/2}}{(\log \log \log t)\cdot \log t}]\log \frac{\xi (t)}{t}=-C\quad a.s ...
Erdős, Paul, Révész, P.
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The Limit Law of the Iterated Logarithm
Journal of Theoretical Probability, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Law of Iterated Logarithm for Parabolic SPDEs
1999We prove a version of Strassen’s functional law of iterated logarithm for a family of parabolic SPDEs. The lack of scaling due to the Green function makes it impossible to reduce the proof to the comparison of one single process at several times.
Millet, Annie, Chenal, Fabien
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