Zobrazeno 1 - 10
of 114
pro vyhledávání: '"Sang, Hailin"'
Publikováno v:
Comptes Rendus. Mathématique, Vol 358, Iss 6, Pp 701-712 (2020)
Renz [13] has established a rate of convergence $1/\sqrt{n}$ in the central limit theorem for martingales with some restrictive conditions. In the present paper a modification of the methods, developed by Bolthausen [2] and Grama and Haeusler [6], is
Externí odkaz:
https://doaj.org/article/5523f100c5f044768e97e53ac72e16d8
Autor:
Hasan, Mahmud, Sang, Hailin
The generative adversarial network (GAN) is an important model developed for high-dimensional distribution learning in recent years. However, there is a pressing need for a comprehensive method to understand its error convergence rate. In this resear
Externí odkaz:
http://arxiv.org/abs/2310.15387
We establish the asymptotic theory of least absolute deviation estimators for AR(1) processes with autoregressive parameter satisfying $n(\rho_n-1)\to\gamma$ for some fixed $\gamma$ as $n\to\infty$, which is parallel to the results of ordinary least
Externí odkaz:
http://arxiv.org/abs/2301.02291
Let $\{X_n: n\in \N\}$ be a linear process with density function $f(x)\in L^2(\R)$. We study wavelet density estimation of $f(x)$. Under some regular conditions on the characteristic function of innovations, we achieve, based on the number of nonzero
Externí odkaz:
http://arxiv.org/abs/2211.09594
Autor:
Beknazaryan, Aleksandr, Sang, Hailin
We consider regression estimation with modified ReLU neural networks in which network weight matrices are first modified by a function $\alpha$ before being multiplied by input vectors. We give an example of continuous, piecewise linear function $\al
Externí odkaz:
http://arxiv.org/abs/2207.08306
Limit theorems for linear random fields with innovations in the domain of attraction of a stable law
In this paper we study the convergence in distribution and the local limit theorem for the partial sums of linear random fields with i.i.d. innovations that have infinite second moment and belong to the domain of attraction of a stable law with index
Externí odkaz:
http://arxiv.org/abs/2109.03688
Deep learning (DL) has gained much attention and become increasingly popular in modern data science. Computer scientists led the way in developing deep learning techniques, so the ideas and perspectives can seem alien to statisticians. Nonetheless, i
Externí odkaz:
http://arxiv.org/abs/2102.01194
In this paper we propose a variable bandwidth kernel regression estimator for $i.i.d.$ observations in $\mathbb{R}^2$ to improve the classical Nadaraya-Watson estimator. The bias is improved to the order of $O(h_n^4)$ under the condition that the fif
Externí odkaz:
http://arxiv.org/abs/2101.04783
Autor:
Fortune, Timothy, Sang, Hailin
In this paper, we estimate the Shannon entropy $S(f) = -\E[ \log (f(x))]$ of a one-sided linear process with probability density function $f(x)$. We employ the integral estimator $S_n(f)$, which utilizes the standard kernel density estimator $f_n(x)$
Externí odkaz:
http://arxiv.org/abs/2009.03472
In this paper, we establish a local limit theorem for linear fields of random variables constructed from independent and identically distributed innovations each with finite second moment. When the coefficients are absolutely summable we do not restr
Externí odkaz:
http://arxiv.org/abs/2007.05036