Bootstrapping Lasso Estimators

By A. Chatterjee, Soumendra Nath Lahiri. 2011

302 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Economics and Econometrics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/59a45558657e93aed40a2f5c73bbd50a8d76dda0

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Citations in the corpus

Confidence intervals for high-dimensional inverse covariance estimation (2014, background): “We note that existing work on statistical inference in high dimensional settings has mostly focused on inference for parameters in linear models and generalized linear models [15, 17, 8, 6, 3, 2, 10].”
Model confidence bounds for variable selection (2016, methodology): “In addition, Chatterjee and Lahiri (2011) show that, using residual bootstrap, the sampling distribution of the Adaptive Lasso estimate 𝜽 can be consistently estimated by the sampling distribution of the bootstrap estimate 𝜽(𝑏).”
Review and evaluation of penalised regression methods for risk prediction in low‐dimensional data with few events (2015, methodology): “[31] and Sortari [15] suggested modified bootstrap methods, but their improvements mostly apply only in linear models.”
Scaling Up Crowd-Sourcing to Very Large Datasets: A Case for Active Learning (2014, background): “Interestingly, even for lasso classiers, there is a modied version of bootstrap that can produce consistent estimates [10].”
Asymptotic Properties of Lasso+mLS and Lasso+Ridge in Sparse High-dimensional Linear Regression (2013, methodology): “Our analysis is not limited to adopting the Lasso in the selection stage, but is applicable to any other model selection criteria with exponentially decay rates of the probability of selecting wrong models, for example, stability selection [38], SCAD [21, 34] and Dantzig selector [12, 9, 26].”
Identifying demand effects in a large network of product categories (2015, methodology): “The Lasso method is well established (Buhlmann and van de Geer, 2011; Chatterjee and Lahiri, 2011) and shows good performance in various applied fields (Wu et al., 2009; Fan et al., 2011).”
On asymptotically optimal confidence regions and tests for high-dimensional models (2013, methodology): “Nevertheless, in the low-dimensional setting, a modified bootstrap scheme has been proposed; [13] and [14] have recently proposed a residual based bootstrap scheme.”
Honest confidence regions and optimality in high-dimensional precision matrix estimation (2015, methodology): “Further alternative methods for inference in the linear model have been proposed and studied in Javanmard and Montanari (2014), Belloni et al. (2014) and bootstrapping approach was suggested in Chatterjee and Lahiri (2013), Chatterjee and Lahiri (2011).”
Estimation and Accuracy after Model Selection (2013, background): “See also Bühlmann and Yu (2002), Definition 1.2, for an asymptotic statement of what is being estimated by a model-selection procedure.”
Subgroup Identification and Variable Selection from Randomized Clinical Trial Data. (2013, methodology): “In particular, for a given data set, we employ the adaptive LASSO-based residual bootstrap (ARB) approach discussed by Chatterjee and Lahiri [2011] to obtain many, say M , bootstrap data sets.”
A Transaction-Cost Perspective on the Multitude of Firm Characteristics (2020, unknown): “…the characteristics that were not removed in the first stage, but now without a lasso constraint, thus circumventing the concerns highlighted in Chatterjee and Lahiri (2011), and apply a bootstrap method to establish which of these characteristics have parametric portfolio weights that are…”
INFERENCE AFTER MODEL AVERAGING IN LINEAR REGRESSION MODELS (2018, unknown): “We follow Chatterjee and Lahiri (2011) and use a residual bootstrap method to construct the confidence intervals for the adaptive LASSO estimator; see Chatterjee and Lahiri (2013) for the higher-order refinement of the bootstrap method, and Camponovo (2015) for a pairs bootstrap method for LASSO est”
Bootstrap Methods in Econometrics (2018, unknown): “The bootstrap does not estimate this distribution consistently (Chatterjee and Lahiri 2011).”
Bootstrapping and sample splitting for high-dimensional, assumption-lean inference (2016, methodology): “While this is a larger literature than can be addressed completely here, it includes early work on model selection [35] and model averaging interpretations [31]; the impossibility results of [38] and [16] on random X and model misspecification; methods based on resampling or sample splitting [18, 19”
High-dimensional simultaneous inference with the bootstrap (2016, methodology): “2014; Javanmard and Montanari 2014; Meinshausen 2015; Foygel Barber and Candès 2015) and some of these extend to generalized linear models. For a recent overview, see also Dezeure et al. (2015). We focus in this paper on a linear model Y = Xβ0 + ε, where we use the notation Y for the n × 1 response ”
Preconditioning the Lasso for sign consistency (2015, methodology): “Bootstrapping techniques such as Chatterjee and Lahiri (2011) left multiply the regression equation by a random diagonal matrix.”
Goodness‐of‐fit tests for high dimensional linear models (2015, methodology): “Some work related to ours here is that of Chatterjee and Lahiri (2010, 2011), Camponovo (2015) and Zhou (2014) who studied the use of the bootstrap with the (adaptive) lasso for constructing confidence sets for the regression coefficients. Work that is more closely aligned to our aim of creating dia”
Rates of convergence of the Adaptive LASSO estimators to the Oracle distribution and higher order refinements by the bootstrap (2013, methodology): “Variants of this condition has been used in the literature, particularly in the context of the Lasso; see Meinshausen and Yu (2009), Huang, Horowitz and Ma (2008), Chatterjee and Lahiri (2011a), and the references therein.”