The Lasso for High Dimensional Regression with a Possible Change Point

Lee, Sokbae; Seo, Myung Hwan; Shin, Youngki

doi:10.1111/rssb.12108

Cited by 98 publications

(137 citation statements)

References 43 publications

(84 reference statements)

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“…This is exactly the model that Lee et al (2012) studied in the case where m can be much larger than n. We shall be more specific about the probabilistic assumptions in Section 3.1. Let J(α 0 ) = {j = 1, ..., 2m : α 0 = 0} be the indices of the non-zero coefficients with cardinality |J(α 0 )|.…”

Section: Scaled Lasso For Threshold Regressionmentioning

confidence: 99%

“…In this section we recall the assumptions used by Lee et al (2012) in their Theorems 2 and 3 which are used as ingredients in the proofs of our Theorems 1 and 2. To be precise, we use the oracle inequalities for the ℓ 1 estimation errors ofα andτ provided by Lee et al (2012).…”

Section: Assumptionsmentioning

confidence: 99%

“…In the random design considered in this paper we require assumption 2 of Lee et al (2012) above to be valid with probability tending to one. However, this is an unnecessarily high-level assumption as it can often be verified by assuming that Σ(τ ) satisfies the uniform restricted eigenvalue condition (which it does in particular when it has full rank -as is in turns true under Assumption 1 if Σ has full rank as argued on page A4 in Lee et al (2012)) and by showing that 1 n X ′ (τ )X(τ ) is uniformly close to Σ(τ ).…”

Section: Assumptionsmentioning

confidence: 99%

“…To be precise, we use the oracle inequalities for the ℓ 1 estimation errors ofα andτ provided by Lee et al (2012). We alter their assumptions slightly, as we are working in a random design as opposed to their fixed regressor design.…”

Section: Assumptionsmentioning

confidence: 99%

“…First, we establish an upper bound on the ℓ ∞ estimation error of the scaled Lasso estimator of Lee et al (2012). This is a non-trivial task as the literature on high-dimensional models has focused almost exclusively on ℓ 1 and ℓ 2 estimation errors.…”

Section: Introductionmentioning

confidence: 99%

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Sharp Threshold Detection based on Sup-Norm Error Rates in High-Dimensional Models

et al. 2015

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We propose a new estimator, the thresholded scaled Lasso, in high dimensional threshold regressions. First, we establish an upper bound on the ℓ ∞ estimation error of the scaled Lasso estimator of Lee et al. (2012). This is a non-trivial task as the literature on high-dimensional models has focused almost exclusively on ℓ 1 and ℓ 2 estimation errors. We show that this supnorm bound can be used to distinguish between zero and non-zero coefficients at a much finer scale than would have been possible using classical oracle inequalities. Thus, our sup-norm bound is tailored to consistent variable selection via thresholding.Our simulations show that thresholding the scaled Lasso yields substantial improvements in terms of variable selection. Finally, we use our estimator to shed further empirical light on the long running debate on the relationship between the level of debt (public and private) and GDP growth.

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Section: Scaled Lasso For Threshold Regressionmentioning

confidence: 99%

Section: Assumptionsmentioning

confidence: 99%

Section: Assumptionsmentioning

confidence: 99%

Section: Assumptionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sharp Threshold Detection based on Sup-Norm Error Rates in High-Dimensional Models

et al. 2015

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Post selection shrinkage estimation for high‐dimensional data analysis

Gao

Ahmed

Feng

2016

Appl Stoch Models Bus & Ind

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In high-dimensional data settings where p n, many penalized regularization approaches were studied for simultaneous variable selection and estimation. However, with the existence of covariates with weak effect, many existing variable selection methods, including Lasso and its generations, cannot distinguish covariates with weak and no contribution. Thus, prediction based on a subset model of selected covariates only can be inefficient. In this paper, we propose a post selection shrinkage estimation strategy to improve the prediction performance of a selected subset model. Such a post selection shrinkage estimator (PSE) is data-adaptive and constructed by shrinking a post selection weighted ridge estimator in the direction of a selected candidate subset. Under an asymptotic distributional quadratic risk criterion, its prediction performance is explored analytically. We show that the proposed post selection PSE performs better than the post selection weighted ridge estimator. More importantly, it improves the prediction performance of any candidate subset model selected from most existing Lasso-type variable selection methods significantly. The relative performance of the post selection PSE is demonstrated by both simulation studies and real data analysis.

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Efficient multiple change point detection for high‐dimensional generalized linear models

et al. 2022

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Change point detection for high‐dimensional data is an important yet challenging problem for many applications. In this article, we consider multiple change point detection in the context of high‐dimensional generalized linear models, allowing the covariate dimension p to grow exponentially with the sample size n. The model considered is general and flexible in the sense that it covers various specific models as special cases. It can automatically account for the underlying data generation mechanism without specifying any prior knowledge about the number of change points. Based on dynamic programming and binary segmentation techniques, two algorithms are proposed to detect multiple change points, allowing the number of change points to grow with n. To further improve the computational efficiency, a more efficient algorithm designed for the case of a single change point is proposed. We present theoretical properties of our proposed algorithms, including estimation consistency for the number and locations of change points as well as consistency and asymptotic distributions for the underlying regression coefficients. Finally, extensive simulation studies and application to the Alzheimer's Disease Neuroimaging Initiative data further demonstrate the competitive performance of our proposed methods.

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The Lasso for High Dimensional Regression with a Possible Change Point

Cited by 98 publications

References 43 publications

Sharp Threshold Detection based on Sup-Norm Error Rates in High-Dimensional Models

Sharp Threshold Detection based on Sup-Norm Error Rates in High-Dimensional Models

Post selection shrinkage estimation for high‐dimensional data analysis

Efficient multiple change point detection for high‐dimensional generalized linear models

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