Berry-Esseen Type bound of a sequence and its application

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• 作者：Yoon Tae Kim ^{ytkim@hallym.ac.kr" class="auth_mail" title="E-mail the corresponding author} ; Hyun Suk Park ; ^{hspark@hallym.ac.kr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 60H07 ; secondary ; 60F25
• 刊名：Journal of the Korean Statistical Society
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：45
• 期：4
• 页码：544-556
• 全文大小：447 K

文摘

Using the recent results obtained by combining Malliavin calculus and Stein’s method, we obtain the Berry–Esseen type bound of a sequence of the random variables of the form class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1226319215301381&_mathId=si2.gif&_user=111111111&_pii=S1226319215301381&_rdoc=1&_issn=12263192&md5=5c050a89f1359419f815f1831d8e2c23">class="imgLazyJSB inlineImage" height="31" width="84" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S1226319215301381-si2.gif">class="mathContainer hidden">class="mathCode">$\{\frac{X_N}{Y_N},N\in \mathbb{N}\}$, where class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1226319215301381&_mathId=si3.gif&_user=111111111&_pii=S1226319215301381&_rdoc=1&_issn=12263192&md5=515bae3ee0edab70007a673ab0303d70" title="Click to view the MathML source">X_Nclass="mathContainer hidden">class="mathCode">$X_N$ and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1226319215301381&_mathId=si4.gif&_user=111111111&_pii=S1226319215301381&_rdoc=1&_issn=12263192&md5=33f2622fd20c4de5a23e688e0460a412" title="Click to view the MathML source">Y_Nclass="mathContainer hidden">class="mathCode">$Y_N$ are square integrable random variables such that their Malliavin derivatives also are square integrable. The aim of this paper is to develop the new techniques, allowing us to obtain sharp Berry–Esseen bound. As an application, we will discuss the rate of convergence of the distribution of the maximum likelihood estimator of a parameter appearing in a stochastic partial differential equation.