arXiv subjects

Yudan Xiong

Publications and source records attributed to Yudan Xiong.

3 recordsLinked to original sources

arXiv2025

Limit theorems for functionals of linear processes in critical regions

Let $X=\{X_n: n\in\mathbb{N}\}$ be the linear process defined by $X_n=\sum^{\infty}_{j=1} a_j\varepsilon_{n-j}$, where the coefficients $a_j=j^{-β}\ell(j)$ are constants with $β>0$ and $\ell$ a slowly varying function, and the innovations $\{\varepsilon_n\}_{n\in\mathbb{Z}}$ are i.i.d. random variables belonging to the domain of attraction of an $α$-stable law with $α\in(0,2]$. Limit theorems for the partial sum $ S_{[Nt]}=\sum^{[Nt]}_{n=1}[K(X_n)-\mathbb{E}K(X_n)]$ with proper measurable functions $K$ have been extensively studied, except for two critical regions: I. $α\in(1,2),β=1$ and II. $αβ=2,β\geq1$. In this paper, we address these open scenarios and identify the asymptotic distributions of $S_{[Nt]}$ under mild conditions.

math.PR↗

arXiv2024

Kernel entropy estimation for linear processes II

Let $X=\{X_n: n\in \mathbb{N}\}$ be a linear process with bounded probability density function $f(x)$. Under certain conditions, we use the kernel estimator \[ \frac{2}{n(n-1)h_n} \sum_{1\le i<j\le n}K\Big(\frac{X_i-X_j}{h_n}\Big) \] to estimate the quadratic functional of $\int_{\mathbb{R}}f^2(x)dx$ of the linear process $X=\{X_n: n\in \mathbb{N}\}$ and improve the corresponding results in [4].

math.ST↗

arXiv2023

Limit theorems for functionals of long memory linear processes with infinite variance

Let $X=\{X_n: n\in\mathbb{N}\}$ be a long memory linear process in which the coefficients are regularly varying and innovations are independent and identically distributed and belong to the domain of attraction of an $α$-stable law with $α\in (0, 2)$. Then, for any integrable and square integrable function $K$ on $\mathbb{R}$, under certain mild conditions, we establish the asymptotic behavior of the partial sum process \[ \left\{\sum\limits_{n=1}^{[Nt]}\big[K(X_n)-\E K(X_n)\big]:\; t\geq 0\right\} \] as $N$ tends to infinity, where $[Nt]$ is the integer part of $Nt$ for $t\geq 0$.

math.PR↗