[Yuima-commits] r228 - pkg/yuimadocs/inst/doc/JSS

[noreply at r-forge.r-project.org]

Author: iacus
Date: 2013-02-07 09:45:59 +0100 (Thu, 07 Feb 2013)
New Revision: 228

Modified:
   pkg/yuimadocs/inst/doc/JSS/article-new.Rnw
   pkg/yuimadocs/inst/doc/JSS/bibliography.bib
Log:
various update

Modified: pkg/yuimadocs/inst/doc/JSS/article-new.Rnw
===================================================================
--- pkg/yuimadocs/inst/doc/JSS/article-new.Rnw	2013-02-07 08:37:50 UTC (rev 227)
+++ pkg/yuimadocs/inst/doc/JSS/article-new.Rnw	2013-02-07 08:45:59 UTC (rev 228)
@@ -1442,7 +1442,15 @@
 A two stage change-point estimation approach is also possible as explained in  \citet{iacyos09}.
 
 \subsection{LASSO Model Selection}
-{\bf STEFANO: EXPLAIN WHAT LASSO MEANS}\par
+The Least Absolute Shrinkage and Selection Operator (LASSO) is a useful and well studied approach to the problem of model selection and its major advantage is the simultaneous execution of both parameter estimation and variable selection (see \citet{Tib96}; \citet{Knight00}; \citet{Efron}). 
+
+To simplify the idea: take a full specified regression model
+$$ Y = \theta_0 +  \theta_1 X_1+  \theta_2 X_2 + \cdots +  \theta_k X_k$$
+perform least squares estimation under $L_1$ constraints, i.e.
+
+$$\hat\theta = \arg\min_\theta \left\{(Y-\theta X)^T (Y-\theta X) + \sum_{i=1}^k |\theta_i|\right\}$$ 
+
+model selection occurs when some of the $\theta_i$ are estimated as zeros. The same idea can be applied to diffusion processes.
 Let $X_t$ be a  diffusion process solution to
 $$
 \de X_t = a( X_t,\alpha) \de t + b(X_t,\beta)  \de W_t

Modified: pkg/yuimadocs/inst/doc/JSS/bibliography.bib
===================================================================
--- pkg/yuimadocs/inst/doc/JSS/bibliography.bib	2013-02-07 08:37:50 UTC (rev 227)
+++ pkg/yuimadocs/inst/doc/JSS/bibliography.bib	2013-02-07 08:45:59 UTC (rev 228)
@@ -64,9 +64,36 @@
     pages={1--23}
 }
 
+ at article{Knight00,
+	author={Knight, K., Fu, W.},
+	title={Asymptotics for lasso-type estimators},
+	journal={Annals of Statistics},
+	year= {2000},
+    number={28},
+    pages={1536--1378}
+}
 
+ at article{Efron,
+	author={Efron, B.,  Hastie, T., Johnstone, I., Tibshirani, R.},
+	title={Least angle regression},
+	journal={Annals of Statistics},
+	year= {2004},
+    number={32},
+    pages={407--489}
+}
 
 
+
+ at article{Tib96,
+	author={Tibshirani, R.},
+	title={Regression shrinkage and selection via the Lasso},
+	journal={J. Roy. Statist. Soc. Ser. B},
+	year= {1996},
+    number={58},
+    pages={267--288}
+}
+
+
 @article{Kessler97,
 author={Kessler, M.}, 
 title={Estimation of an Ergodic Diffusion from Discrete Observations},