Segmented Model Selection in Quantile Regression Using the Minimum Description Length Principle

Aue, Alexander; Cheung, Rex C. Y.; Lee, Thomas C.; Zhong, Ming

doi:10.1080/01621459.2014.889022

Cited by 33 publications

(27 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, recent years have witnessed a renaissance in change-point inference motivated by several applications which require computationally fast and statistically efficient finding of potentially many change-points in large data sets, see e.g. Olshen et al (2004), Siegmund (2013) and Behr et al (2018) for its relevance to cancer genetics, Chen and Zhang (2015) for network analysis, Aue et al (2014) for econometrics, and Hotz et al (2013) for electrophysiology, to name a few. This challenges statistical methodology due to the multiscale nature of these problems (i.e.…”

Section: Introductionmentioning

confidence: 99%

Multiscale change-point segmentation: beyond step functions

Li¹,

Guo²,

Munk³

2019

Electron. J. Statist.

View full text Add to dashboard Cite

Modern multiscale type segmentation methods are known to detect multiple changepoints with high statistical accuracy, while allowing for fast computation. Underpinning theory has been developed mainly for models that assume the signal as a piecewise constant function. In this paper this will be extended to certain function classes beyond such step functions in a nonparametric regression setting, revealing certain multiscale segmentation methods as robust to deviation from such piecewise constant functions. Our main finding is the adaptation over such function classes for a universal thresholding, which includes bounded variation functions, and (piecewise) Hölder functions of smoothness order 0 < α ≤ 1 as special cases. From this we derive statistical guarantees on feature detection in terms of jumps and modes. Another key finding is that these multiscale segmentation methods perform nearly (up to a logfactor) as well as the oracle piecewise constant segmentation estimator (with known jump locations), and the best piecewise constant approximants of the (unknown) true signal. Theoretical findings are examined by various numerical simulations.MSC 2010 subject classifications: 62G08, 62G20, 62G35.

show abstract

Section: Introductionmentioning

confidence: 99%

Multiscale change-point segmentation: beyond step functions

Li¹,

Guo²,

Munk³

2019

Electron. J. Statist.

View full text Add to dashboard Cite

show abstract

“…Second, we contribute a computationally efficient test statistic for testing the existence of a change point. Although there are many tests developed on determining the existence of a change point in linear regression (Andrews, 1993; Bai, 1996; Hansen, 1996), quantile regression (Qu, 2008; Li et al, 2011; Aue et al, 2014; Zhang et al, 2014), transformation models (Kosorok and Song, 2007), time series models (Chan, 1993; Cho and White, 2007), no analogous tests have been developed in the context of robust bent line regression. Our test is motivated from the test for structural change in regression quantiles (Qu, 2008).…”

Section: Introductionmentioning

confidence: 99%

Robust bent line regression

Zhang

2017

Journal of Statistical Planning and Inference

View full text Add to dashboard Cite

We introduce a rank-based bent linear regression with an unknown change point. Using a linear reparameterization technique, we propose a rank-based estimate that can make simultaneous inference on all model parameters, including the location of the change point, in a computationally efficient manner. We also develop a score-like test for the existence of a change point, based on a weighted CUSUM process. This test only requires fitting the model under the null hypothesis in absence of a change point, thus it is computationally more efficient than likelihood-ratio type tests. The asymptotic properties of the test are derived under both the null and the local alternative models. Simulation studies and two real data examples show that the proposed methods are robust against outliers and heavy-tailed errors in both parameter estimation and hypothesis testing.

show abstract

“…Contributions in a different direction from ours include [5], who considered the estimation of structural breaks in the median of an underlying regression model by means of least absolute deviations. In the quantile regression framework, Aue et al [1] have recently developed a related methodology to perform segmented variable selection that includes break point detection as a special case. The focus of the present paper, however, is more on the aspects of nonlinear time series analysis.…”

Section: Introductionmentioning

confidence: 99%

Piecewise quantile autoregressive modeling for nonstationary time series

Aue¹,

Cheung²,

Lee³

et al. 2017

Bernoulli

Self Cite

View full text Add to dashboard Cite

We develop a new methodology for the fitting of nonstationary time series that exhibit nonlinearity, asymmetry, local persistence and changes in location scale and shape of the underlying distribution. In order to achieve this goal, we perform model selection in the class of piecewise stationary quantile autoregressive processes. The best model is defined in terms of minimizing a minimum description length criterion derived from an asymmetric Laplace likelihood. Its practical minimization is done with the use of genetic algorithms. If the data generating process follows indeed a piecewise quantile autoregression structure, we show that our method is consistent for estimating the break points and the autoregressive parameters. Empirical work suggests that the proposed method performs well in finite samples.Comment: Published at http://dx.doi.org/10.3150/14-BEJ671 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

show abstract

Segmented Model Selection in Quantile Regression Using the Minimum Description Length Principle

Cited by 33 publications

References 32 publications

Multiscale change-point segmentation: beyond step functions

Multiscale change-point segmentation: beyond step functions

Robust bent line regression

Piecewise quantile autoregressive modeling for nonstationary time series

Contact Info

Product

Resources

About