Berry-Esseen bounds for self-normalized sums of locally dependent random variables

The Berry-Esseen bound provides an upper bound on the Kolmogorov distance between a random variable and the normal distribution.In this paper,we establish Berry-Esseen bounds with optimal rates for self-normalized sums of locally dependent random variables,assuming only a second-moment condition.Our proof leverages Stein's method and introduces a novel randomized concentration inequality,which may also be of independent interest for other applications.Our main results have applied to self-normalized sums of m-dependent random variables and graph dependency models.

Local Dependence Test Between Random Vectors Based on the Robust Conditional Spearman's ρ and Kendall's τ

This paper introduces two local conditional dependence matrices based on Spearman'sρand Kendall'sτgiven the condition that the underlying random variables belong to the intervals determined by their quantiles.The robustness is studied by means of the influence functions of conditional Spearman'sρand Kendall'sτ.Using the two matrices,we construct the corresponding test statistics of local conditional dependence and derive their limit behavior including consistency,null and alternative asymptotic distributions.Simulation studies illustrate a superior power performance of the proposed Kendall-based test.Real data analysis with proposed methods provides a precise description and explanation of some financial phenomena in terms of mathematical statistics.

Infinite Clusters in Locally Dependent Percolation on Z^d

Techniques of Burton-Keane,developed earlier for independent percolation on Zd,are adapted to the setting of locally dependent percolation on Zd for d 2.The main result of this paper is a uniqueness theorem,that there exists almost surely a unique infinite out-cluster in locally dependent percolation on Zd,under the finite energy condition.

Three Elements That Affect the Realisation of Subject-Verb Agreement in the Speech Production of L2 Speakers of English with L1 Chinese

The experiment presented in this research is targeting a ＇positional＇ stage of a ＇modular＇ model of speech production originally proposed by Levelt （1989）, Bock ＆ Levelt （1994）, where selected lemmas are inserted into syntactic frames. Results suggest a difference between L1 and L2 English speakers at the positional stage. While this might suggest that the speech planning process is different in native and non-native speakers, an alternative view is also proposed that the observed differences are the result of differences in the way that linguistic forms are stored, rather than a fundamental difference in the way that speech is planned. This result indicates main verb, copula be ＆ local dependency effect are the three elements that affect the realization of English subject-verb agreement, and helps us locate the phase where L2 subject-verb agreement errors happen.

Theoretical XANES spectra for C_(76)isomers

Two isolated pentagon rule satisfying isomers of C76 are optimized. And 1（D2） isomer is reconfirmed to be the relative more stable one. The X-ray absorption near-edge structure （XANES） spectra are theoretically characterized by the hybrid density functional theory （DFT） method in combination with the full core-hole potentials. Isomer identification of XANES spectra for Cr6 is found and XANES spectra dependence on local structure of fullerene is discussed.