A note on the asymptotic distribution of LASSO estimator for correlated data
- Shuva Gupta
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The asymptotic distribution of the Lasso estimator for regression models with independent errors has been investigated by Knight and Fu (2000). In this note we extend these results to regression models with a general weak dependence structure. We determine the asymptotic distribution of the Lasso estimator when the number of parameters M is fixed and the number of observations, n, converges to infinity. We show that, for an appropriate choice of the tuning parameter of the method, this asymptotic distribution reduces to a multivariate normal distribution. As an illustrative example, the special case of AR(1) is also investigated.
- Bunea, F. (2008). Honest variable selection in linear and logistic regression models via ℓ1 and ℓ1 + ℓ2 penalization. Electron. J. Stat., 2, 1153–1194. CrossRef
- Bunea, F., Tsybakov, A. and Wegkamp, M. (2007). Sparsity oracle inequalities for the Lasso. Electron. J. Stat., 1, 169–194. CrossRef
- Coulon-Prieur, C. and Doukhan, P. (2000). A triangular central limit theorem under a new weak dependence condition. Statist. Probab. Lett., 47, 61–68. CrossRef
- Dedecker, J., et al. (2007). Weak Dependence: With Examples and Applications, Lecture Notes in Statistics (Vol. 190). Springer, New York.
- Doukhan, P. and Louhichi, S. (1999). A new weak dependence condition and applications to moment inequalities. Stochastic Process. Appl., 84(2), 313–342. CrossRef
- Germain, J.-F. and Roueff, F. (2010). Weak convergence of the regularization path in penalized M-Estimation. Scand. J. Stat.
- Knight, K. and Fu, W. (2000). Asymptotics for lasso-type estimators. Ann. Statist., 28, 1356–1378. CrossRef
- Meinshausen, N. and Bühlmann, P. (2006) High-dimensional graphs and variable selection with the lasso. Ann. Statist., 34, 1436–1462. CrossRef
- Shorack, G. (2000). Probability for Statisticians, Springer Texts in Statistics. Springer-Verlag, New York.
- Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B, 58, 267–288.
- Van Der Vaart, A. and Wellner, J. (1996). Weak convergence and empirical processes, Springer Series in Statistics. Springer-Verlag, New York.
- Wainwright, M. (2007). Information-theoretic limits on sparse signal recovery: Dense versus sparse measurement matrices, Technical Report. University of California Berkley.
- Wang, H., Li, G. and Tsai, C.-L. (2007). Regression coefficient and autoregressive order shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B, 69, 63–78.
- Zhao, P. and Yu, B. (2006). On model selection consistency of Lasso. J. Mach. Learn. Res., 7, 2541–2563.
- A note on the asymptotic distribution of LASSO estimator for correlated data
Volume 74, Issue 1 , pp 10-28
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links
- Primary 62J07
- Secondary 60F15, 62E20
- Penalized regression
- weak dependence
- central limit theorem
- asymptotic distribution
- Shuva Gupta (1)
- Author Affiliations
- 1. Division of Statistics, Department of Mathematics, Northern Illinois University, De Kalb, IL, USA