I am a Reader in the Department of Statistics, University of Warwick and a Turing Fellow at the Alan Turing Institute, previously an Associate Professor in the University of Warwick, a Lecturer in the University of Bristol, a postdoc of Professor Richard Samworth and a graduate student of Professor Zhiliang Ying. I obtained my academic degrees from Fudan University (B.Sc. in Mathematics, June 2009 and Ph.D. in Mathematical Statistics, June 2013).
Abstract
This paper concerns about the limiting distributions of change point
estimators, in a high-dimensional linear regression time series context, where
a regression object $(y_t, X_t) \in \mathbb{R} \times \mathbb{R}^p$ is observed
at every time point $t \in \{1, \ldots, n\}$. At unknown time points, called
change points, the regression coefficients change, with the jump sizes measured
in $\ell_2$-norm. We provide limiting distributions of the change point
estimators in the regimes where the minimal jump size vanishes and where it
remains a constant. We allow for both the covariate and noise sequences to be
temporally dependent, in the functional dependence framework, which is the
first time seen in the change point inference literature. We show that a
block-type long-run variance estimator is consistent under the functional
dependence, which facilitates the practical implementation of our derived
limiting distributions. We also present a few important byproducts of their own
interest, including a novel variant of the dynamic programming algorithm to
boost the computational efficiency, consistent change point localisation rates
under functional dependence and a new Bernstein inequality for data possessing
functional dependence. The paper is available at http://arxiv.org/abs/2207.12453
I am a Reader in the Department of Statistics, University of Warwick and a Turing Fellow at the Alan Turing Institute, previously an Associate Professor in the University of Warwick, a Lecturer in the University of Bristol, a postdoc of Professor Richard Samworth and a graduate student of Professor Zhiliang Ying. I obtained my academic degrees from Fudan University (B.Sc. in Mathematics, June 2009 and Ph.D. in Mathematical Statistics, June 2013).
Abstract
This paper concerns about the limiting distributions of change point
estimators, in a high-dimensional linear regression time series context, where
a regression object $(y_t, X_t) \in \mathbb{R} \times \mathbb{R}^p$ is observed
at every time point $t \in \{1, \ldots, n\}$. At unknown time points, called
change points, the regression coefficients change, with the jump sizes measured
in $\ell_2$-norm. We provide limiting distributions of the change point
estimators in the regimes where the minimal jump size vanishes and where it
remains a constant. We allow for both the covariate and noise sequences to be
temporally dependent, in the functional dependence framework, which is the
first time seen in the change point inference literature. We show that a
block-type long-run variance estimator is consistent under the functional
dependence, which facilitates the practical implementation of our derived
limiting distributions. We also present a few important byproducts of their own
interest, including a novel variant of the dynamic programming algorithm to
boost the computational efficiency, consistent change point localisation rates
under functional dependence and a new Bernstein inequality for data possessing
functional dependence. The paper is available at http://arxiv.org/abs/2207.12453