Optimal Change-point Testing for High-dimensional Linear Models with Temporal Dependence
@inproceedings{Wang2022OptimalCT, title={Optimal Change-point Testing for High-dimensional Linear Models with Temporal Dependence}, author={Daren Wang and Zifeng Zhao}, year={2022} }
This paper studies change-point testing for high-dimensional linear models, an important problem that is not well explored in the literature. Specifically, we propose a quadratic-form-based cumulative sum (CUSUM) test to inspect the stability of the regression coefficients in a high-dimensional linear model. The proposed test is able to control the type-I error at any desired level and is theoretically sound for temporally dependent observations. We establish the asymptotic distribution of the…
2 Citations
High-dimensional data segmentation in regression settings permitting heavy tails and temporal dependence
- Computer Science
- 2022
A data segmentation methodology for the high-dimensional linear regression problem where the regression parameters are allowed to undergo multiple changes with good performance in comparative simulation studies and also in applications to climate science and economic datasets.
Detecting Abrupt Changes in Sequential Pairwise Comparison Data
- Computer Science
- 2022
This paper proposes novel and practicable algorithms based on dynamic programming that can consistently estimate the unknown locations of the change points in a high-dimensional BTL model with piece-wise constant parameters.
References
SHOWING 1-10 OF 41 REFERENCES
Uniform change point tests in high dimension
- Mathematics
- 2015
Consider $d$ dependent change point tests, each based on a CUSUM-statistic. We provide an asymptotic theory that allows us to deal with the maximum over all test statistics as both the sample size…
Testing for Change Points in Time Series
- Mathematics
- 2010
This article considers the CUSUM-based (cumulative sum) test for a change point in a time series. In the case of testing for a mean shift, the traditional Kolmogorov–Smirnov test statistic involves a…
Most Powerful Test Against a Sequence of High Dimensional Local Alternatives
- MathematicsSSRN Electronic Journal
- 2021
We propose a powerful quadratic test for the overall significance of many weak exogenous variables in a dense autoregressive model. By shrinking the classical weighting matrix on the sample moments…
The lasso for high dimensional regression with a possible change point
- Mathematics, Computer ScienceJournal of the Royal Statistical Society. Series B, Statistical methodology
- 2016
It is established conditions under which the estimation error of the unknown threshold parameter can be bounded by a factor that is nearly n−1 even when the number of regressors can be much larger than the sample size n.
Oracle Estimation of a Change Point in High-Dimensional Quantile Regression
- MathematicsJournal of the American Statistical Association
- 2018
ABSTRACT In this article, we consider a high-dimensional quantile regression model where the sparsity structure may differ between two sub-populations. We develop ℓ1-penalized estimators of both…
Break detection in the covariance structure of multivariate time series models
- Mathematics
- 2009
In this paper, we introduce an asymptotic test procedure to assess the stability of volatilities and cross-volatilites of linear and nonlinear multivariate time series models. The test is very…
Randomized tests for high-dimensional regression: A more efficient and powerful solution
- Computer ScienceNeurIPS
- 2020
This paper proposes a testing procedure that blends the classical $F$-test with a random projection step, and shows that the proposed test achieves sharp adaptive rates and is proved to be minimax optimal.
Estimating and testing linear models with multiple structural changes
- Mathematics
- 1995
This paper develops the statistical theory for testing and estimating multiple change points in regression models. The rate of convergence and limiting distribution for the estimated parameters are…
A More Powerful Two-Sample Test in High Dimensions using Random Projection
- Mathematics, Computer ScienceNIPS
- 2011
This work proposes a new test statistic for the two-sample test of means that integrates a random projection with the classical Hotelling T2 statistic, and derives an asymptotic power function for this test, and demonstrates superior performance against competing tests in the parameter regimes anticipated by the theoretical results.
Structural Breaks in Time Series
- Economics, MathematicsOxford Research Encyclopedia of Economics and Finance
- 2019
This article covers methodological issues related to estimation, testing, and computation for models involving structural changes, and focuses on the so-called off-line methods whereby one wants to retrospectively test for breaks in a given sample of data and form confidence intervals about the break dates.