We propose a multivariate sparse group lasso variable selection and estimation method for data with high-dimensional predictors as well as high-dimensional response variables. The method is carried out through a penalized multivariate multiple linear regression model with an arbitrary group structure for the regression coefficient matrix. It suits many biology studies well in detecting associations between multiple traits and multiple predictors, with each trait and each predictor embedded in some biological functional groups such as genes, pathways or brain regions. The method is able to effectively remove unimportant groups as well as unimportant individual coefficients within important groups, particularly for large p small n problems, and is flexible in handling various complex group structures such as overlapping or nested or multilevel hierarchical structures. The method is evaluated through extensive simulations with comparisons to the conventional lasso and group lasso methods, and is applied to an eQTL association study.
This paper applies the Least Absolute Shrinkage and Selection Operator (LASSO) to make rolling one‐minute‐ahead return forecasts using the entire cross‐section of lagged returns as candidate predictors. The LASSO increases both out‐of‐sample fit and forecast‐implied Sharpe ratios. This out‐of‐sample success comes from identifying predictors that are unexpected, short‐lived, and sparse. Although the LASSO uses a statistical rule rather than economic intuition to identify predictors, the predictors it identifies are nevertheless associated with economically meaningful events: the LASSO tends to identify as predictors stocks with news about fundamentals.
more » « less- NSF-PAR ID:
- 10079585
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- The Journal of Finance
- Volume:
- 74
- Issue:
- 1
- ISSN:
- 0022-1082
- Format(s):
- Medium: X Size: p. 449-492
- Size(s):
- p. 449-492
- Sponsoring Org:
- National Science Foundation
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This paper studies the asymptotic properties of the penalized least squares estimator using an adaptive group Lasso penalty for the reduced rank regression. The group Lasso penalty is defined in the way that the regression coefficients corresponding to each predictor are treated as one group. It is shown that under certain regularity conditions, the estimator can achieve the minimax optimal rate of convergence. Moreover, the variable selection consistency can also be achieved, that is, the relevant predictors can be identified with probability approaching one. In the asymptotic theory, the number of response variables, the number of predictors and the rank number are allowed to grow to infinity with the sample size. Copyright © 2016 John Wiley & Sons, Ltd.
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