The Berry–Esséen type bound of sample quantiles for strong mixing sequence

Yang, Wenzhi; Hu, Shuhe; Wang, Xuejun; Ling, Nengxiang

doi:10.1016/j.jspi.2011.09.004

Cited by 19 publications

(10 citation statements)

References 20 publications

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“…If the underlying sequence

{({}, X_{k})}_{k \in Z}

is α ‐mixing with polynomial rate and satisfies some additional regularity conditions, Lahiri and Sun () established the optimal rate n −1/2 . Variations of this result under weaker conditions were obtained in Yang et al () and Yang et al (), but in this case, only suboptimal rates ( n −1/6 log n and lower) were reached. Despite its generality, the concept of strong mixing has some serious deficits.…”

Section: Introductionsupporting

confidence: 51%

Optimal Rate of Convergence for Empirical Quantiles and Distribution Functions for Time Series

Jirak

2016

Journal Time Series Analysis

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Given a stationary sequence ¹X k º k2Z , we are interested in the rate of convergence in the central limit theorem of the empirical quantiles and the empirical distribution function. Under a general notion of weak dependence, we show a Berry-Esseen result with optimal rate n 1=2 . The setup includes many prominent time series models, such as functions of ARMA or (augmented) GARCH processes. In this context, optimal Berry-Esseen rates for empirical quantiles appear to be novel.

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“…If the underlying sequence

{({}, X_{k})}_{k \in Z}

Section: Introductionsupporting

confidence: 51%

Optimal Rate of Convergence for Empirical Quantiles and Distribution Functions for Time Series

Jirak

2016

Journal Time Series Analysis

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“…A classical problem in asymptotic statistics is the assessment of the speed of convergence to Gaussianity (that is, the computation of explicit Berry-Esseen bounds) for parametric and nonparametric estimation procedures -for recent references connected to the main topic of the present paper, see for instance [17,29,55]. In this area, an important novel development is given by the derivation of effective Berry-Esseen bounds by means of the combination of two probabilistic techniques, namely the Malliavin calculus of variations and the Stein's method for probabilistic approximations.…”

Section: Motivation and Overviewmentioning

confidence: 99%

Normal approximations for wavelet coefficients on spherical Poisson fields

Durastanti

Marinucci

Peccati

2014

Journal of Mathematical Analysis and Applications

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a b s t r a c tWe compute explicit upper bounds on the distance between the law of a multivariate Gaussian distribution and the joint law of wavelet/needlet coefficients based on a homogeneous spherical Poisson field. In particular, we develop some results from Peccati and Zheng (2010) [42], based on Malliavin calculus and Stein's methods, to assess the rate of convergence to Gaussianity for a triangular array of needlet coefficients with growing dimensions. Our results are motivated by astrophysical and cosmological applications, in particular related to the search for point sources in Cosmic Rays data.

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“…They used a martingale approximation in their procedure. Yang et al (2012) investigated a Berry-Esseen type bound for the sample quantiles of a strongly mixing sequence.…”

Section: Introductionmentioning

confidence: 99%

A Berry-Esseen Type Bound in Kernel Density Estimation for a Random Left-Truncation Model

Asghari¹,

Fakoor²,

Sarmad³

2014

Communications for Statistical Applications and Methods

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In this paper we derive a Berry-Esseen type bound for the kernel density estimator of a random left truncated model, in which each datum (Y) is randomly left truncated and is sampled if Y ≥ T , where T is the truncation random variable with an unknown distribution. This unknown distribution is estimated with the Lynden-Bell estimator. In particular the normal approximation rate, by choice of the bandwidth, is shown to be close to n −1/6 modulo logarithmic term. We have also investigated this normal approximation rate via a simulation study.

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The Berry–Esséen type bound of sample quantiles for strong mixing sequence

Cited by 19 publications

References 20 publications

Optimal Rate of Convergence for Empirical Quantiles and Distribution Functions for Time Series

Optimal Rate of Convergence for Empirical Quantiles and Distribution Functions for Time Series

Normal approximations for wavelet coefficients on spherical Poisson fields

A Berry-Esseen Type Bound in Kernel Density Estimation for a Random Left-Truncation Model

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