The Optimal Estimation of Lasso

Huiyi Xia

doi:doi:10.11648/j.sjams.20150306.19

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The Optimal Estimation of Lasso

Huiyi Xia

Published in Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 6)

Received: 30 December 2015 Accepted: Published: 30 December 2015

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Abstract

The estimation of lasso is important problem of high dimensional data; the optimal estimation’s formula of lasso is unsolved riddle of high dimensional data. In order to solve this problem, we give the structure of lasso estimation by using mathematical method in the orthogonal design. The optimal estimation’s formula of lasso is solved in the orthogonal design, it is pointed out that there is a gradual process of dimension reduction by using method of lasso.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 6)
DOI	10.11648/j.sjams.20150306.19
Page(s)	293-297
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Lasso, Estimation, Solution

References

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[2]	B. Efron, T. Hastie, I. “Johnstone and R. Tibshirani. Least Angle Regression,” The Annals of Statistics 2004, Vol. 32. No. 2, pp: 407-499.
[3]	J. Fan and R. Li. “Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties,” Journal of the American Statistical Association. 2001, Vol. 96, No. 456, pp: 1348-1360.
[4]	K. Knight, W. Fu. “Asymptotics for Lasso-Type Estimators,” The Annals of Statistics. 2000, Vol.28, No. 5, pp: 1356-1378.
[5]	H. Zou, H. Zhang, “On the Adaptive Elastic-net with a Diverging Number of Parameters” The Annals of Statistics. 2009, 37(4), pp: 1733–1751.
[6]	D. Donohu, I. Johnstone, “Ideal spatial adaption by wavelet shinkage,” Biometrica. 1994, 81, pp: 425-455.
[7]	H. Zou, T. Hastie, “Regularization and variable selection via the elastic net,” Journal of the Royal Statistical Society. 2005, Series B, 67(2), pp: 301-320.
[8]	R. Tibshirani, M. Saunders, S. Rossrt, J. Zhu, K. Knight, “Sparsity and smoothness via the fused lasso,” Journal of the Royal Statistical Society. 2005, Series B, 67(1), pp: 91-108.
[9]	L. Wasserman, K. Roeder, “HIGH-DIMENSIONAL VARIABLE SELECTION,” The Annals of Statistics. 2009, 37(5A), pp: 2718–2201.
[10]	E. Austin, W. Pan, X. Shen, “Penalized Regression and Risk Prediction in Genome-Wide Association Studies,” Stat Anal Data Min. 2013, 6(4), pp: 1: 23.
[11]	L. Wu, Y. Yang, H. Liu, “Nonnegative-lasso and in index tracking,” Computational Statistics and Data Analysis. 2014, 70, pp: 116-126.
[12]	F. Bunea, J. Leder, Y. She, “The Group Square-Root Lasso: Theoretical Properties and Fast Algorithms,” Information Theory IEEE Transactions on. 2013, 60(2), pp: 1313-1325.
[13]	A. Ahrens, A. Bhattacharjee, “Two-Step Lasso Estimation of the Spatial weighs Matrix,” Econometrics. 2015, 3, pp: 128-155.

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Huiyi Xia. (2015). The Optimal Estimation of Lasso. Science Journal of Applied Mathematics and Statistics, 3(6), 293-297. https://doi.org/10.11648/j.sjams.20150306.19

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ACS Style

Huiyi Xia. The Optimal Estimation of Lasso. Sci. J. Appl. Math. Stat. 2015, 3(6), 293-297. doi: 10.11648/j.sjams.20150306.19

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AMA Style

Huiyi Xia. The Optimal Estimation of Lasso. Sci J Appl Math Stat. 2015;3(6):293-297. doi: 10.11648/j.sjams.20150306.19

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@article{10.11648/j.sjams.20150306.19,
  author = {Huiyi Xia},
  title = {The Optimal Estimation of Lasso},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {3},
  number = {6},
  pages = {293-297},
  doi = {10.11648/j.sjams.20150306.19},
  url = {https://doi.org/10.11648/j.sjams.20150306.19},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20150306.19},
  abstract = {The estimation of lasso is important problem of high dimensional data; the optimal estimation’s formula of lasso is unsolved riddle of high dimensional data. In order to solve this problem, we give the structure of lasso estimation by using mathematical method in the orthogonal design. The optimal estimation’s formula of lasso is solved in the orthogonal design, it is pointed out that there is a gradual process of dimension reduction by using method of lasso.},
 year = {2015}
}

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TY  - JOUR
T1  - The Optimal Estimation of Lasso
AU  - Huiyi Xia
Y1  - 2015/12/30
PY  - 2015
N1  - https://doi.org/10.11648/j.sjams.20150306.19
DO  - 10.11648/j.sjams.20150306.19
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 293
EP  - 297
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20150306.19
AB  - The estimation of lasso is important problem of high dimensional data; the optimal estimation’s formula of lasso is unsolved riddle of high dimensional data. In order to solve this problem, we give the structure of lasso estimation by using mathematical method in the orthogonal design. The optimal estimation’s formula of lasso is solved in the orthogonal design, it is pointed out that there is a gradual process of dimension reduction by using method of lasso.
VL  - 3
IS  - 6
ER  -

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Author Information

Huiyi Xia

Department of Mathematics and Computer Science, Chizhou University, Anhui, China

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Plain Text BibTeX RIS

APA Style

Huiyi Xia. (2015). The Optimal Estimation of Lasso. Science Journal of Applied Mathematics and Statistics, 3(6), 293-297. https://doi.org/10.11648/j.sjams.20150306.19

Copy | Download

ACS Style

Huiyi Xia. The Optimal Estimation of Lasso. Sci. J. Appl. Math. Stat. 2015, 3(6), 293-297. doi: 10.11648/j.sjams.20150306.19

Copy | Download

AMA Style

Huiyi Xia. The Optimal Estimation of Lasso. Sci J Appl Math Stat. 2015;3(6):293-297. doi: 10.11648/j.sjams.20150306.19

Copy | Download

@article{10.11648/j.sjams.20150306.19,
  author = {Huiyi Xia},
  title = {The Optimal Estimation of Lasso},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {3},
  number = {6},
  pages = {293-297},
  doi = {10.11648/j.sjams.20150306.19},
  url = {https://doi.org/10.11648/j.sjams.20150306.19},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20150306.19},
  abstract = {The estimation of lasso is important problem of high dimensional data; the optimal estimation’s formula of lasso is unsolved riddle of high dimensional data. In order to solve this problem, we give the structure of lasso estimation by using mathematical method in the orthogonal design. The optimal estimation’s formula of lasso is solved in the orthogonal design, it is pointed out that there is a gradual process of dimension reduction by using method of lasso.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - The Optimal Estimation of Lasso
AU  - Huiyi Xia
Y1  - 2015/12/30
PY  - 2015
N1  - https://doi.org/10.11648/j.sjams.20150306.19
DO  - 10.11648/j.sjams.20150306.19
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 293
EP  - 297
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20150306.19
AB  - The estimation of lasso is important problem of high dimensional data; the optimal estimation’s formula of lasso is unsolved riddle of high dimensional data. In order to solve this problem, we give the structure of lasso estimation by using mathematical method in the orthogonal design. The optimal estimation’s formula of lasso is solved in the orthogonal design, it is pointed out that there is a gradual process of dimension reduction by using method of lasso.
VL  - 3
IS  - 6
ER  -

Copy | Download