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A law of the iterated logarithm for error density estimator in censored linear regression

Journal of nonparametric statistics (Print), 2022
We 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
semanticscholar   +1 more source

Lower deviations in β-ensembles and law of iterated logarithm in last passage percolation

Israel Journal of Mathematics, 2019
For 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
semanticscholar   +1 more source

A remark on elephant random walks via the classical law of the iterated logarithm for self-similar Gaussian processes

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
semanticscholar   +1 more source

Law of the Iterated Logarithm for 𝑘/2-Permanental Processes and the Local Times of Related Markov Processes

Memoirs of the American Mathematical Society
Let Y Y be a symmetric ...
Michael Marcus, Jay Rosen
semanticscholar   +1 more source

Law of the iterated logarithm for error density estimators in nonlinear autoregressive models

Communications in Statistics - Theory and Methods, 2020
In 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
semanticscholar   +1 more source

The Law of Iterated Logarithm

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
openaire   +1 more source

On the law of the iterated logarithm. I

Indagationes Mathematicae (Proceedings), 1955
Die 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
openaire   +2 more sources

A new law of iterated logarithm

Acta Mathematica Hungarica, 1990
The 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.
openaire   +1 more source

The Limit Law of the Iterated Logarithm

Journal of Theoretical Probability, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Law of Iterated Logarithm for Parabolic SPDEs

1999
We 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
openaire   +2 more sources

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