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The law of iterated logarithm for the estimations of diffusion-type processes
Advances in Difference Equations, 2020 This paper mainly discusses the asymptotic behaviours on the lasso-type estimators for diffusion-type processes with a small noise. By constructing the objective function on the estimation, in view of convexity argument, it is proved that the estimator ...
Mingzhi Mao, Gang Huang
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Annales Mathematicae Silesianae, 2021 In this paper our considerations are focused on some Markov chain associated with certain piecewise-deterministic Markov process with a statedependent jump intensity for which the exponential ergodicity was obtained in [4].
Kubieniec Joanna
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Asymptotics for the Moment Convergence of U-Statistics in LIL
Journal of Inequalities and Applications, 2010 Let Un be a U-statistic based on a symmetric kernel h(x,y) and i.i.d. samples {X,Xn;n≥1}. In this paper, the exact moment convergence rates in the law of the iterated logarithm and the law of the logarithm of Un are obtained, which extend previous
Ke-Ang Fu
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Zhejiang Daxue xuebao. Lixue ban, 2000 The aim of this paper is to establish a law of the iterated logarithm for non-stationary weakly negatively associated random vectors in under the finite second moment.
RUANHong-shun(阮宏顺) +2 more
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The law of the iterated logarithm for exchangeable random variables
International Journal of Mathematics and Mathematical Sciences, 1995 In this note, necessary and sufficient conditions for laws of the iterated logarithm are developed for exchangeable random variables.
Hu-Ming Zhang, Robert L. Taylor
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On Feller's criterion for the law of the iterated logarithm
International Journal of Mathematics and Mathematical Sciences, 1994 Combining Feller's criterion with a non-uniform estimate result in the context of the Central Limit Theorem for partial sums of independent random variables, we obtain several results on the Law of the Iterated Logarithm.
Deli Li, M. Bhaskara Rao, Xiangchen Wang
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Laws of the k-Iterated Logarithm of Weighted Sums in a Sub-Linear Expected Space
MathematicsThe law of the iterated logarithm precisely refines the law of large numbers and plays a fundamental role in probability limit theory. The framework of sub-linear expectation spaces substantially extends the classical concept of probability spaces.
Xiang Zeng
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Representations for Integral Functionals of Kernel Density Estimators
Austrian Journal of Statistics, 2016 We establish a representation as a sum of independent random variables, plus a remainder term, for estimators of integral functionals of the density function, which have a certain simple structure.
David M. Mason
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On the other law of the iterated logarithm for self-normalized sums
Anais da Academia Brasileira de Ciências, 2008 Inthisnote, we obtain a Chung's integral test for self-normalized sums of i.i.d. random variables. Furthermore, we obtain a convergence rate of Chung law of the iterated logarithm for self-normalized sums.Nesta nota, obtemos um teste integral de Chung ...
Guang-Hui Cai
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Discrete Dynamics in Nature and Society, 2022 Let X,Xn,n≥1 be a sequence of independent, identically distributed random variables under sublinear expectations with CVX20 and an=olog logn−d, we obtain the exact rates in the law of iterated logarithm of a kind of weighted infinite series of CVMn−ε+anσ¯
Mingzhou Xu, Kun Cheng
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