Nonnegative Elastic Net and application in index tracking

Wu, Lan; Yang, Yuehan

doi:10.1016/j.amc.2013.11.049

Cited by 36 publications

(27 citation statements)

References 22 publications

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“… 2014 ). Many other nonnegative sparse estimators have been proposed such as Yang and Wu ( 2016 ), Wu and Yang ( 2014 ), Mandal and Ma ( 2016 ), Li et al. ( 2019 ), Xie and Yang ( 2019 ), Li and Yang ( 2019 ), etc..…”

Section: Motivagting Examplesmentioning

confidence: 99%

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Penalized and constrained LAD estimation in fixed and high dimension

Ran

Yang

2021

Stat Papers

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Recently, many literatures have proved that prior information and structure in many application fields can be formulated as constraints on regression coefficients. Following these work, we propose a L 1 penalized LAD estimation with some linear constraints in this paper. Different from constrained lasso, our estimation performs well when heavy-tailed errors or outliers are found in the response. In theory, we show that the proposed estimation enjoys the Oracle property with adjusted normal variance when the dimension of the estimated coefficients p is fixed. And when p is much greater than the sample size n, the error bound of proposed estimation is sharper than k log( p)/n. It is worth noting the result is true for a wide range of noise distribution, even for the Cauchy distribution. In algorithm, we not only consider an typical linear programming to solve proposed estimation in fixed dimension , but also present an nested alternating direction method of multipliers (ADMM) in high dimension. Simulation and application to real data also confirm that proposed estimation is an effective alternative when constrained lasso is unreliable.

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Section: Motivagting Examplesmentioning

confidence: 99%

“…Because stock index tracking requires both sparse and nonnegative constraints, many nonnegative constrained penalty estimates have been proposed recently, include Wu et al. ( 2014 ), Yang and Wu ( 2016 ), Wu and Yang ( 2014 ), Li et al. ( 2019 ), etc..…”

Section: Real Data Applicationsmentioning

confidence: 99%

Penalized and constrained LAD estimation in fixed and high dimension

Ran

Yang

2021

Stat Papers

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“…As future work, an extended analysis of feature selection could bring a trade-off between model complexity (in terms of number of variables) and performance for all the classes. In addition to this, non-negative linear models [65] can be explored to focus on model interpretability.…”

Section: Comparison Of H-lr Model To Fcbf Feature Selectionmentioning

confidence: 99%

Partial order label decomposition approaches for melanoma diagnosis

Sánchez‐Monedero

Pérez-Ortiz

Sáez

et al. 2018

Applied Soft Computing

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Melanoma is a type of cancer that develops from the pigment-containing cells known as melanocytes. Usually occurring on the skin, early detection and diagnosis is strongly related to survival rates. Melanoma recognition is a challenging task that nowadays is performed by well trained dermatologists who may produce varying diagnosis due to the task complexity. This motivates the development of automated diagnosis tools, in spite of the inherent difficulties (intra-class variation, visual similarity between melanoma and non-melanoma lesions, among others). In the present work, we propose a system combining

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“…, β p . Concerning adapting to this real world constraint, Wu et al [29] and Wu and Yang [28] introduced nonnegative lasso and nonnegative elastic net approaches, which are successfully applied to solve the real world index tracking problem without short sales (this corresponds to the nonnegative-value constraint on weights). There exist more such range constraints on the regression coefficients in the real world problems, therefore more flexible models are needed to address problems that require arbitrary-range constraints on the regression coefficients.…”

Section: Introductionmentioning

confidence: 99%

Variable Selection and Regularization via Arbitrary Rectangle-range Generalized Elastic Net

Ding¹,

Peng²,

Song³

et al. 2021

Preprint

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We introduce the arbitrary rectangle-range generalized elastic net penalty method, abbreviated to ARGEN, for performing constrained variable selection and regularization in high-dimensional sparse linear models. As a natural extension of the nonnegative elastic net penalty method, ARGEN is proved to have variable selection consistency and estimation consistency under some conditions. The asymptotic behavior in distribution of the ARGEN estimators have been studied. We also propose an algorithm called MU-QP-RR-W-l1 to efficiently solve ARGEN. By conducting simulation study we show that ARGEN outperforms the elastic net in a number of settings. Finally an application of S&P 500 index tracking with constraints on the stock allocations is performed to provide general guidance for adapting ARGEN to solve real-world problems.

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Nonnegative Elastic Net and application in index tracking

Cited by 36 publications

References 22 publications

Penalized and constrained LAD estimation in fixed and high dimension

Penalized and constrained LAD estimation in fixed and high dimension

Partial order label decomposition approaches for melanoma diagnosis

Variable Selection and Regularization via Arbitrary Rectangle-range Generalized Elastic Net

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