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The law of iterated logarithm of Rescaled Range Statistics for AR(1) Model

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Acta Mathematica Sinica,English Series 2006年第2期22卷 535-544页

作者： Zheng Yan LIN Sung Chul LEE Department of Mathematics Zhejiang University Department of Mathematics Yonsei University

Let {Xn,n ≥ 0} be an AR（1） process. Let Q（n） be the rescaled range statistic, or the R/S statistic for {Xn} which is given by （max1≤k≤n（∑j=1^k（Xj - ^-Xn）） - min 1≤k≤n（∑j=1^k（ Xj - ^Xn ））） /（n ^-1∑j=1^n（Xj -^-Xn）^2）^1/2 where ^-Xn = n^-1 ∑j=1^nXj. In this paper we show a law of iterated logarithm for rescaled range statistics Q（n） for AR（1） model.

关键词： Rescaled range statistics law of iterated logarithm AR(1) model

THE law of iterated logarithm FOR R/S STATISTICS

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Acta Mathematica Scientia 2005年第2期25卷 326-330页

作者：林正炎 Department of Mathematics Zhejiang University Xixi CampusHangzhou 310028China

A law of iterated logarithm for R/S statistics with the help of the strong approximations of R/S statistics by functions of a Wiener process is shown.

关键词： R/S statistics law of iterated logarithm strong approximation

A NONCLASSICAL law of iterated logarithm FOR NEGATIVELY ASSOCIATED RANDOM VARIABLES

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Applied Mathematics(A Journal of Chinese Universities) 2003年第2期18卷 200-208页

作者： Jiang YeDept. of Math., Zhejiang University,Hangzhou 310028. Dept. of Math. Zhejiang University Hangzhou

A nonclassical law of iterated logarithm that holds for a stationary negatively associated sequence of random variables with finite variance is proved in this paper. The proof is based on a Rosenthal type maximal ineq... 详细信息

关键词： negative dependence law of iterated logarithm nonclassical law of iterated logarithm.

PRECISE RATE IN THE law OF iterated logarithm FOR ρ-MIXING SEQUENCE

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Applied Mathematics(A Journal of Chinese Universities) 2003年第4期18卷 482-488页

作者： Huang Wei Zhang Lixin Jiang YeDept.of Math.,Zhejiang Univ.,Hangzhou 310028,China. Dept. of Math. Zhejiang Univ. Hangzhou China

Let {X,X n;n≥1} be a strictly stationary sequence of ρ-mixing random variables with mean zero and finite variance. Set S n=n k=1X k,M n=max k≤n｜S k｜,n≥1. Suppose lim n→∞ES2 n/n=∶σ2>0 and ∞n=1ρ 2/d(2n)2(b+1),if b≥0. It is proved that,for any b>-1, limε0ε 2(b+1)∞n=1(loglogn)bnlognP{M n≥εσ2nloglogn}= 2(b+1)πГ(b+3/2)∞k=0(-1)k(2k+1) 2b+2,where Г(·) is a Gamma function.

关键词： mixing random variable law of iterated logarithm tail probabilities

Precise Rates in the Generalized law of the iterated logarithm in Rm

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Journal of Mathematical Research with Applications 2018年第1期38卷 103-110页

作者： Mingzhou XU Yunzheng DING Yongzheng ZHOU School of Information and Engineering Jingdezhen Ceramic University

Let {X, X_n, n ≥ 1} be a sequence of i.i.d. random vectors with EX =（0,..., 0）m×1and Cov（X, X） = σ2Ⅰm, and set S_n =∑i=1~n Xi, n ≥ 1. For every d > 0 and a_n =o(（log log n）-d), the article deals with the precise rates in the genenralized law of the iterated logarithm for a kind of weighted infinite series of P(|S_n| ≥（ε + a_n）σn1/2（log log n）d).

关键词： precise rates law of iterated logarithm complete convergence i.i.d. random vectors

The law of the iterated logarithm for the Sums of φ-Mixing Sequences with Duple Suffixes

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Chinese Quarterly Journal of Mathematics 1992年第4期7卷 68-71页

作者：杨善朝 Guangxi Normal University

Hu Shuhe gets a sufficient condition on the law of the iterated logarithm for the sums of φ-mixing sequences with duple suffixes. This paper greatly improves his condition.

关键词： φ-Mixing Sequences Sum of Double Suffix Sequences law of iterated logarithm

KERNEL ESTIMATION OF HIGHER DERIVATIVES OF DENSITY AND HAZARD RATE FUNCTION FOR TRUNCATED AND CENSORED DEPENDENT DATA

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Acta Mathematica Scientia 2003年第4期23卷 477-486页

作者：陈清平戴永隆 Department of Statistics Wuhan University Wuhan 430072 China 2. Wuhan University of Science and Technology Wuhan 430081 China Department of Statistics Zhongshan University Guangzhou 510275 China

Based on left truncated and right censored dependent data, the estimators of higher derivatives of density function and hazard rate function are given by kernel smoothing method. When observed data exhibit α-mixing dependence, local properties including strong consistency and law of iterated logarithm are presented. Moreover, when the mode estimator is defined as the random variable that maximizes the kernel density estimator, the asymptotic normality of the mode estimator is established.

关键词： Truncated and censored data α-mixing strong consistency law of iterated logarithm mode

STRONG CONVERGENCE RATES OF SEVERAL ESTIMATORS IN SEMIPARAMETRIC VARYING-COEFFICIENT PARTIALLY LINEAR MODELS

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Acta Mathematica Scientia 2009年第5期29卷 1113-1127页

作者：周勇尤进红王晓婧 Academy of Mathematics and Systems Science Chinese Academy of Science Department of Statistics Shanghai University of Finance and Economics Department of Biostatistics University of North Carolina at Chapel Hill Chapel Hill NC USA

This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang （2005） proposed a profile least squares estimator for the parametric component and established its asymptotic normality. We further show that the profile least squares estimator can achieve the law of iterated logarithm. Moreover, we study the estimators of the functions characterizing the non-linear part as well as the error variance. The strong convergence rate and the law of iterated logarithm are derived for them, respectively.

关键词： partially linear regression model varying-coefficient profile leastsquares error variance strong convergence rate law of iterated logarithm

How big are the increments of G-Brownian motion?

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Science China Mathematics 2014年第8期57卷 1687-1700页

作者： HU Feng CHEN ZengJing ZHANG DeFei School of Mathematical Sciences Qufu Normal University School of Mathematics Shandong University Department of Financial Engineering Ajou University Department of Mathematics Honghe University

In this paper,we investigate the problem:How big are the increments of G-Brownian *** obtain the Csrg and R′ev′esz’s type theorem for the increments of G-Brownian *** applications of this result,we get the law of iterated logarithm and the Erds and R′enyi law of large numbers for G-Brownian ***,it turns out that our theorems are natural extensions of the classical results obtained by Csrg and R′ev′esz(1979).

关键词： sublinear expectation capacity G-normal distribution G-Brownian motion increments of GBrownian motion law of iterated logarithm