Explanipedia

Research on the influence laws of traffic and temperature loads on the strain responses of urban girder bridges Open

Wenting Qiao, Yongcheng Qi, Yang Liu · 2025

Largest Eigenvalues of Principal Minors of Deformed Gaussian Orthogonal Ensembles and Wishart Matrices Open

Tiefeng Jiang, Yongcheng Qi · 2024

Consider a high-dimensional Wishart matrix $\bd{W}=\bd{X}^T\bd{X}$ where the entries of $\bd{X}$ are i.i.d. random variables with mean zero, variance one, and a finite fourth moment $η$. Motivated by problems in signal processing and high-…

Eigenvalues of Product of Ginibre Ensembles and Their Inverses and that of Truncated Haar Unitary Matrices and Their Inverses Open

Shuhua Chang, Tiefeng Jiang, Yongcheng Qi · 2024

Consider two types of products of independent random matrices, including products of Ginibre matrices and inverse Ginibre matrices and products of truncated Haar unitary matrices and inverse truncated Haar matrices. Each product matrix has…

Limiting distributions of the likelihood ratio test statistics for independence of normal random vectors Open

Mingyue Hu, Yongcheng Qi · 2022

Consider the likelihood ratio test (LRT) statistics for the independence of sub-vectors from a $p$-variate normal random vector. We are devoted to deriving the limiting distributions of the LRT statistics based on a random sample of size $…

Inference of high quantiles of a heavy-tailed distribution from block data Open

Yongcheng Qi, Mengzi Xie, Jingping Yang · 2022

In this paper we consider the estimation problem for high quantiles of a heavy-tailed distribution from block data when only a few largest values are observed within blocks. We propose estimators for high quantiles and prove that these est…

Some results on probabilities of moderate deviations Open

Deli Li, Yu Miao, Yongcheng Qi · 2022

Let $\{X, X_{n}; n \geq 1\}$ be a sequence of i.i.d. non-degenerate real-valued random variables with $\mathbb{E}X^{2} < \infty$. Let $S_{n} = \sum_{i=1}^{n} X_{i}$, $n \geq 1$. Let $g(\cdot): ~[0, \infty) \rightarrow [0, \infty)$ be a non…

Empirical likelihood method for complete independence test on high-dimensional data Open

Yongcheng Qi, Yingchao Zhou · 2022

Given a random sample of size $n$ from a $p$ dimensional random vector, where\nboth $n$ and $p$ are large, we are interested in testing whether the $p$\ncomponents of the random vector are mutually independent. This is the so-called\ncompl…

Pearson's goodness-of-fit tests for sparse distributions Open

Shuhua Chang, Deli Li, Yongcheng Qi · 2021

Pearson's chi-squared test is widely used to test the goodness of fit between categorical data and a given discrete distribution function. When the number of sets of the categorical data, say k, is a fixed integer, Pearson's chi-squ…

Asymptotic Distributions for Likelihood Ratio Tests for the Equality of Covariance Matrices Open

Wenchuan Guo, Yongcheng Qi · 2021

Consider $k$ independent random samples from $p$-dimensional multivariate normal distributions. We are interested in the limiting distribution of the log-likelihood ratio test statistics for testing for the equality of $k$ covariance matri…

Limiting Empirical Spectral Distribution for Products of Rectangular Matrices Open

Yongcheng Qi, Hongru Zhao · 2021

In this paper, we consider $m$ independent random rectangular matrices whose entries are independent and identically distributed standard complex Gaussian random variables and assume the product of the $m$ rectangular matrices is an $n$ by…

Discussion on paper ‘On studying extreme values and systematic risks with nonlinear time series models and tail dependence measures’ by Zhengjun Zhang Open

Yongcheng Qi · 2021

I would like to take this opportunity to congratulate Zhengjun for his continuing contribution to extreme-value statistics in recent years. In this review paper, some fundamental theories on univar...

Pearson's goodness-of-fit tests for sparse distributions Open

Shuhua Chang, Deli Li, Yongcheng Qi · 2021

Pearson's chi-squared test is widely used to test the goodness of fit between categorical data and a given discrete distribution function. When the number of sets of the categorical data, say k, is a fixed integer, Pearson's chi-squ…

Limiting Spectral Radii of Circular Unitary Matrices under Light Truncation Open

Yu Miao, Yongcheng Qi · 2020

Consider a truncated circular unitary matrix which is a $p_n$ by $p_n$ submatrix of an $n$ by $n$ circular unitary matrix after deleting the last $n-p_n$ columns and rows. Jiang and Qi \cite{JiangQi2017} and Gui and Qi \cite{GQ2018} study …

Spectral Radii of Products of Random Rectangular Matrices Open

Yongcheng Qi, Mengzi Xie · 2019

We consider m independent random rectangular matrices whose entries are independent and identically distributed standard complex Gaussian random variables. Assume the product of the m rectangular matrices is an n by n square matrix. The ma…

Adjusted Empirical Likelihood Method for the Tail Index of A Heavy-Tailed Distribution Open

Yizeng Li, Yongcheng Qi · 2019

Empirical likelihood is a well-known nonparametric method in statistics and has been widely applied in statistical inference. The method has been employed by Lu and Peng (2002) to constructing confidence intervals for the tail index of a h…

Jackknife Empirical Likelihood Methods Open

Yongcheng Qi · 2018

Since Jing et al. [1] propose the jackknife empirical likelihood method for U-statistics, the method has been developed and applied to inference problems in statistical theory and other areas such as biostatistics, medical statistics and i…

A method for estimating the power of moments Open

Shuhua Chang, Deli Li, Yongcheng Qi, Andrew Rosalsky · 2018

Let X be an observable random variable with unknown distribution function [Formula: see text], [Formula: see text], and let [Formula: see text] We call θ the power of moments of the random variable X. Let [Formula: see…

Limiting Distributions of Spectral Radii for Product of Matrices from the Spherical Ensemble Open

Shuhua Chang, Deli Li, Yongcheng Qi · 2018

Consider the product of $m$ independent $n\times n$ random matrices from the spherical ensemble for $m\ge 1$. The spectral radius is defined as the maximum absolute value of the $n$ eigenvalues of the product matrix. When $m=1$, the limiti…

Spectral Radii of Truncated Circular Unitary Matrices Open

Wenhao Gui, Yongcheng Qi · 2017

Consider a truncated circular unitary matrix which is a $p_n$ by $p_n$ submatrix of an $n$ by $n$ circular unitary matrix by deleting the last $n-p_n$ columns and rows. Jiang and Qi (2017) proved that the maximum absolute value of the eige…

On Tests for Complete Independence of Normal Random Vectors Open

Shuhua Chang, Yongcheng Qi · 2017

Consider a random sample of $n$ independently and identically distributed $p$-dimensional normal random vectors. A test statistic for complete independence of high-dimensional normal distributions, proposed by Schott (2005), is defined as …

A Simple Point Estimator of the Power of Moments Open

Shuhua Chang, Deli Li, Yongcheng Qi, Andrew Rosalsky · 2017

Let $X$ be an observable random variable with unknown distribution function $F(x) = \mathbb{P}(X \leq x), - \infty < x < \infty$, and let \[\ θ= \sup\left \{ r \geq 0:~ \mathbb{E}|X|^{r} < \infty \right \}. \] We call $θ$ the power of mome…

Empirical Distribution of Scaled Eigenvalues for Product of Matrices from the Spherical Ensemble Open

Shuhua Chang, Yongcheng Qi · 2017

Consider the product of $m$ independent $n\times n$ random matrices from the spherical ensemble for $m\ge 1$. The empirical distribution based on the $n$ eigenvalues of the product is called the empirical spectral distribution. Two recent …

Empirical Spectral Distribution for Product of Spherical Ensembles Open

Shuhua Chang, Yongcheng Qi · 2017

Consider the product of $m$ independent $n\times n$ spherical ensembles for $m\ge 1$. The empirical distribution based on the $n$ eigenvalues of the product is called the empirical spectral distribution. A recent paper by Zeng (2016) obtai…

Empirical Distributions of Eigenvalues of Product Ensembles Open

Tiefeng Jiang, Yongcheng Qi · 2015

Assume a finite set of complex random variables form a determinantal point process, we obtain a theorem on the limit of the empirical distribution of these random variables. The result is applied to %We study the limits of the empirical di…

A characterization of a new type of strong law of large numbers Open

Deli Li, Yongcheng Qi, Andrew Rosalsky · 2015

Let and . Let be a sequence of independent copies of a real-valued random variable and set . We say satisfies the -type strong law of large numbers (and write ) if almost surely. This paper is devoted to a characterization of . By app…

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