Sparse High Dimensional Models in Economics

Fan, Jianqing; Lv, Jinchi; Lei, Qi

doi:10.2139/ssrn.1659322

Cited by 89 publications

(99 citation statements)

References 92 publications

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“…For each value of d we conduct 200 iterations of the same procedure: Generate a model, synthesize data from that model, and then calculate estimates based on the synthesized data. In detail, the data are first generated from an elliptical vector autoregressive model (Fan et al, 2011b;Qiu et al, 2015b) of order one and marginal multivariate t-distribution with 5 degrees of freedom. Secondly, 1% of them are further corrupted by a multiplier of independent Unif(1, 15) noise.…”

Section: Simulationmentioning

confidence: 99%

Robust Inference of Risks of Large Portfolios

et al. 2015

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We propose a bootstrap-based robust high-confidence level upper bound (Robust H-CLUB) for assessing the risks of large portfolios. The proposed approach exploits rank-based and quantilebased estimators, and can be viewed as a robust extension of the H-CLUB procedure (Fan et al., 2015). Such an extension allows us to handle possibly misspecified models and heavy-tailed data, which are stylized features in financial returns. Under mixing conditions, we analyze the proposed approach and demonstrate its advantage over H-CLUB. We further provide thorough numerical results to back up the developed theory, and also apply the proposed method to analyze a stock market dataset.

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Section: Simulationmentioning

confidence: 99%

Robust Inference of Risks of Large Portfolios

et al. 2015

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“…In a situation as such, classical inference approaches become invalid or break down. The reader may consult a survey article by [15] for challenges in inference due to high dimensions. Even worse, as the number of graphs involved in a multiple graphical model (MGM), which is often used for modeling networks experiencing stage-wise change due to external forces, grows with the sample size or the number of nodes, estimation and inference become more challenging.…”

Section: Introductionmentioning

confidence: 99%

Large Multiple Graphical Model Inference via Bootstrap

2020

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SummaryLarge economic and financial networks may experience stage-wise change as a result of external shocks. To detect and infer a structural change, we consider an inference problem in the framework of multiple Gaussian graphical models, particularly when the number of graphs and the dimension of a graph expand with the sample size. In such a situation, two major challenges emerge as a result of the bias and uncertainty inherent in regularization, which is required treating such overparameterized models. To deal with these challenges, bootstrap is utilized to approximate the sampling distribution of a likelihood ratio test statistic. Theoretically, we show that the proposed method leads to correct asymptotic inference in a high-dimensional situation regardless of the distribution of the test statistic.Numerically, it compares favorably to its competitors through simulations. Finally, our statistical analysis of the network of 200 stocks reveals that the financial network exhibits a dramatic change in that the interacting units become more connected due to the financial crisis between 2007 and 2009. More importantly, certain units respond more strongly than others, and after the crisis, some alterations fade while others strengthen.

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“…Over the last 10 years, there are a great deal of developments in statistical theory and computing on variable selection techniques for ultrahigh-dimensional feature space, see Hastie et al (2009), Fan et al (2011b, and Bühlmann and van de Geer (2011) for overviews. To reduce dimension, Tibshirani (1996), Fan and Li (2001), Candes and Tao (2007), Bickel et al (2009), Fan and Lv (2011), and Zhang and Zhang (2012) proposed techniques to select variables and estimate parameters simultaneously by solving a high-dimensional optimization problem.…”

Section: Introductionmentioning

confidence: 99%

Conditional sure independence screening by conditional marginal empirical likelihood

Lin²

2015

Ann Inst Stat Math

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In many applications, researchers often know a certain set of predictors is related to the response from some previous investigations and experiences. Based on the conditional information, we propose a conditional screening feature procedure via ranking conditional marginal empirical likelihood ratios. Due to the use of centralized variable, the proposed screening approach works well when there exist either or both hidden important variables and unimportant variables that are highly marginal correlated with the response. Moreover, the new method is demonstrated effective in scenarios with less restrictive distributional assumptions by inheriting the advantage of empirical likelihood approach and is computationally simple because it only needs to evaluate the conditional marginal empirical likelihood ratio at one point, without parameter estimation and iterative algorithm. The theoretical results reveal that the proposed procedure has sure screening properties. The merits of the procedure are illustrated by extensive numerical examples.

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Sparse High Dimensional Models in Economics

Cited by 89 publications

References 92 publications

Robust Inference of Risks of Large Portfolios

Robust Inference of Risks of Large Portfolios

Large Multiple Graphical Model Inference via Bootstrap

Conditional sure independence screening by conditional marginal empirical likelihood

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