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Guangyu Yang

Publications and source records attributed to Guangyu Yang.

29 records · Page 2Linked to original sources
arXiv2023

Least absolute deviation estimation for AR(1) processes with roots close to unity

We establish the asymptotic theory of least absolute deviation estimators for AR(1) processes with autoregressive parameter satisfying $n(ρ_n-1)\toγ$ for some fixed $γ$ as $n\to\infty$, which is parallel to the results of ordinary least squares estimators developed by Andrews and Guggenberger (2008) in the case $γ=0$ or Chan and Wei (1987) and Phillips (1987) in the case $γ\ne 0$. Simulation experiments are conducted to confirm the theoretical results and to demonstrate the robustness of the least absolute deviation estimation.

math.ST↗
arXiv2022

Multi-objective Optimization of Notifications Using Offline Reinforcement Learning

Mobile notification systems play a major role in a variety of applications to communicate, send alerts and reminders to the users to inform them about news, events or messages. In this paper, we formulate the near-real-time notification decision problem as a Markov Decision Process where we optimize for multiple objectives in the rewards. We propose an end-to-end offline reinforcement learning framework to optimize sequential notification decisions. We address the challenge of offline learning using a Double Deep Q-network method based on Conservative Q-learning that mitigates the distributional shift problem and Q-value overestimation. We illustrate our fully-deployed system and demonstrate the performance and benefits of the proposed approach through both offline and online experiments.

cs.LG↗
arXiv2022

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 $0<α\leq2$ under the condition that the innovations are centered if $1<α\leq2$ and are symmetric if $α=1$. We establish these two types of limit theorems as long as the linear random fields are well-defined, the coefficients are either absolutely summable or not absolutely summable.

math.PR↗
arXiv2014

Asymptotic distributions related to mildly-explosive second order autoregressive models

In this paper, we consider the normalized least squares estimator of the parameter in a mildly-explosive first-order autoregressive model with dependent errors which are modeled as a mildly-explosive AR(1) process. We prove that the estimator has a Cauchy limit law which provides a bridge between moderate deviation asymptotics and the earlier results on the local to unity and explosive autoregressive models. In particular, the results can be applied to understand the near-integrated second order autoregressive processes. Simulation studies are also carried out to assess the performance of least squares estimation in finite samples.

math.PR↗
arXiv2013

The probability of rectangular unimodular matrices over $\F_q[x]$

In this note, we compute the probability that a $k\times n$ matrix can be extended to an $n\times n$ invertible matrix over $\F_q[x]$, which turns out to be $(1-q^{k-n})(1-q^{k-1-n})...(1-q^{1-n})$. Connections with Dirichlet's density theorem on the co-prime integers and its various generalizations are also presented.

math.PR↗
arXiv2012

Moderate deviations principle for empirical covariance from a unit root

In the present paper, we consider the linear autoregressive model in $\rr$, $$ X_{k,n}=θ_n X_{k,n-1}+ξ_k, k=0,1,...,n, n\ge 1$$ where $θ_n\in [0,1)$ is unknown, $(ξ_k)_{k\in\zz}$ is a sequence of centered i.i.d. r.v. valued in $\rr$ representing the noise. When $θ_n\to 1$, the moderate deviations principle for empirical covariance is discussed and as statistical applications we provide the moderate deviation estimates of the least square and the Yule-Walker estimators of the parameter $θ_n$.

math.PR↗
arXiv2010

Strassen's invariance principle for random walk in random environment

In this paper, we consider random walk in random environment on $\mathbb{Z}^{d}\,(d\geq1)$ and prove the Strassen's strong invariance principle for this model, via martingale argument and the theory of fractional coboundaries of Derriennic and Lin \cite{DL}, under some conditions which require the variance of the quenched mean has a subdiffusive bound. The results partially fill the gaps between law of large numbers and central limit theorems.

math.PR↗
arXiv2007

The law of the iterated logarithm for additive functionals of Markov chains

In the paper, the law of the iterated logarithm for additive functionals of Markov chains is obtained under some weak conditions, which are weaker than the conditions of invariance principle of additive functionals of Markov chains in M. Maxwell and M. Woodroofe (2000). The main technique is the martingale argument and the theory of fractional coboundaries.

math.PR↗
arXiv2007

A note for extension of almost sure central limit theory

Hörmann (2006) gave an extension of almost sure central limit theorem for bounded Lipschitz 1 function. In this paper, we show that his result of almost sure central limit theorem is also hold for any Lipschitz function under stronger conditions.

math.PR↗