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We propose a new method to construct confidence intervals for quantities that are associated with a stationary time series, which avoids direct estimation of the asymptotic variances. Unlike the existing tuning-parameter-dependent…

Methodology · Statistics 2010-05-13 Xiaofeng Shao

Self-normalized processes are basic to many probabilistic and statistical studies. They arise naturally in the the study of stochastic integrals, martingale inequalities and limit theorems, likelihood-based methods in hypothesis testing and…

Probability · Mathematics 2009-09-29 Victor H. de la Peña , Michael J. Klass , Tze Leung Lai

Motivated by the study of dependent random variables by coupling with independent blocks of variables, we obtain first sufficient conditions for the moderate deviation principle in its functional form for triangular arrays of independent…

Probability · Mathematics 2008-05-07 Florence Merlevede , Magda Peligrad

Stein's method is applied to obtain a general Cramer-type moderate deviation result for dependent random variables whose dependence is defined in terms of a Stein identity. A corollary for zero-bias coupling is deduced. The result is also…

Probability · Mathematics 2013-02-06 Louis H. Y. Chen , Xiao Fang , Qi-Man Shao

The inference procedure for the mean of a stationary time series is usually quite different under various model assumptions because the partial sum process behaves differently depending on whether the time series is short or long-range…

Statistics Theory · Mathematics 2016-03-22 Shuyang Bai , Murad S. Taqqu , Ting Zhang

The term moderate deviations is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability of some random variables to a constant and a weak convergence…

Probability · Mathematics 2024-11-20 Rita Giuliano , Claudio Macci , Barbara Pacchiarotti

We reconsider the choice of renormalization schemes in a differential-equation approach to aid the discussion of the renormalization of the unstable particles and the CKM matrix in the Standard Model. Certain mass dependent schemes do not…

High Energy Physics - Phenomenology · Physics 2007-05-23 Ji-Feng Yang

In this article, we discuss the sharp moderate and large deviations between the quantiles of population and the quantiles of samples. Cram\'{e}r type moderate deviations and Bahadur-Rao type large deviations are established with some mild…

Statistics Theory · Mathematics 2023-10-03 Xiequan Fan

In Stein's method, the exchangeable pair approach is commonly used to estimate the approximation errors in normal approximation. In this paper, we establish a Cram\'er-type moderate deviation theorem of normal approximation for unbounded…

Probability · Mathematics 2022-09-26 Zhuo-Song Zhang

We consider a stable but nearly unstable autoregressive process of any order. The bridge between stability and instability is expressed by a time-varying companion matrix $A_{n}$ with spectral radius $\rho(A_{n}) < 1$ satisfying…

Statistics Theory · Mathematics 2019-10-17 Frédéric Proïa

We study statistical inferences for a class of modulated stationary processes with time-dependent variances. Due to non-stationarity and the large number of unknown parameters, existing methods for stationary, or locally stationary, time…

Statistics Theory · Mathematics 2013-02-04 Zhibiao Zhao , Xiaoye Li

Let $(Z_n)_{n\geq0}$ be a supercritical Galton-Watson process. Consider the Lotka-Nagaev estimator for the offspring mean. In this paper, we establish self-normalized Cram\'{e}r type moderate deviations and Berry-Esseen's bounds for the…

Probability · Mathematics 2023-10-03 Xiequan Fan , Qi-Man Shao

We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…

Probability · Mathematics 2018-11-06 Christoph H. Lampert , Liva Ralaivola , Alexander Zimin

We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…

Methodology · Statistics 2026-01-28 Jinyuan Chang , Yue Du , Jing He , Qiwei Yao

In this paper, we consider moderate deviations for Good's coverage estimator. The moderate deviation principle and the self-normalized moderate deviation principle for Good's coverage estimator are established. The results are also applied…

Statistics Theory · Mathematics 2013-05-10 Fuqing Gao

In this paper, we study the self-normalized Cram\'er-type moderate deviation of the empirical measure of the stochastic gradient Langevin dynamics (SGLD). Consequently, we also derive the Berry-Esseen bound for SGLD. Our approach is by…

Probability · Mathematics 2026-03-04 Hongsheng Dai , Xiequan Fan , Jianya Lu

We give a Cram\'{e}r moderate deviation expansion for martingales with differences having finite conditional moments of order $2+\rho, \rho \in (0,1],$ and finite one-sided conditional exponential moments. The upper bound of the range of…

Probability · Mathematics 2020-05-11 Xiequan Fan , Ion Grama , Quansheng Liu

Two-sample $U$-statistics are widely used in a broad range of applications, including those in the fields of biostatistics and econometrics. In this paper, we establish sharp Cram\'{e}r-type moderate deviation theorems for Studentized…

Statistics Theory · Mathematics 2016-09-29 Jinyuan Chang , Qi-Man Shao , Wen-Xin Zhou

When testing for the mean vector in a high dimensional setting, it is generally assumed that the observations are independently and identically distributed. However if the data are dependent, the existing test procedures fail to preserve…

Statistics Theory · Mathematics 2014-11-17 Deepak Nag Ayyala , Junyong Park , Anindya Roy

This paper proposes self-normalized tests for multistep conditional predictive ability in forecast comparison. By normalizing the sample mean of the transformed loss differential using functionals of its cumulative sum (CUSUM) process,…

Statistics Theory · Mathematics 2026-05-11 Qitong Chen , Shuwen Lai