This commit is contained in:
Morten Hjorth-Jensen
2021-09-08 06:34:56 +02:00
parent 9c3168fd83
commit 5fcdfec57b
6 changed files with 7 additions and 5 deletions
+1 -1
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@@ -649,7 +649,7 @@ which leads to
$$
\hat{\boldsymbol{\beta}}_i^{\mathrm{Lasso}} = \left\{\begin{array}{ccc}y_i-\frac{\lambda}{2} &\mathrm{if} & y_i> \frac{\lambda}{2}\\
y_i+\frac{\lambda}{2} &\mathrm{if} & y_i < -\frac{\lambda}{2}\\
0 &\mathrm{if} & \verty_i\vert\le \frac{\lambda}{2}\end{array}\right.\\.
0 &\mathrm{if} & \vert y_i\vert\le \frac{\lambda}{2}\end{array}\right.\\.
$$
<p>&nbsp;<br>
+1 -1
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@@ -666,7 +666,7 @@ which leads to
$$
\hat{\boldsymbol{\beta}}_i^{\mathrm{Lasso}} = \left\{\begin{array}{ccc}y_i-\frac{\lambda}{2} &\mathrm{if} & y_i> \frac{\lambda}{2}\\
y_i+\frac{\lambda}{2} &\mathrm{if} & y_i < -\frac{\lambda}{2}\\
0 &\mathrm{if} & \verty_i\vert\le \frac{\lambda}{2}\end{array}\right.\\.
0 &\mathrm{if} & \vert y_i\vert\le \frac{\lambda}{2}\end{array}\right.\\.
$$
<p>
+1 -1
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@@ -671,7 +671,7 @@ which leads to
$$
\hat{\boldsymbol{\beta}}_i^{\mathrm{Lasso}} = \left\{\begin{array}{ccc}y_i-\frac{\lambda}{2} &\mathrm{if} & y_i> \frac{\lambda}{2}\\
y_i+\frac{\lambda}{2} &\mathrm{if} & y_i < -\frac{\lambda}{2}\\
0 &\mathrm{if} & \verty_i\vert\le \frac{\lambda}{2}\end{array}\right.\\.
0 &\mathrm{if} & \vert y_i\vert\le \frac{\lambda}{2}\end{array}\right.\\.
$$
<p>
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@@ -764,7 +764,7 @@
"$$\n",
"\\hat{\\boldsymbol{\\beta}}_i^{\\mathrm{Lasso}} = \\left\\{\\begin{array}{ccc}y_i-\\frac{\\lambda}{2} &\\mathrm{if} & y_i> \\frac{\\lambda}{2}\\\\\n",
" y_i+\\frac{\\lambda}{2} &\\mathrm{if} & y_i< -\\frac{\\lambda}{2}\\\\\n",
"\t\t\t\t\t\t\t 0 &\\mathrm{if} & \\verty_i\\vert\\le \\frac{\\lambda}{2}\\end{array}\\right.\\\\.\n",
"\t\t\t\t\t\t\t 0 &\\mathrm{if} & \\vert y_i\\vert\\le \\frac{\\lambda}{2}\\end{array}\\right.\\\\.\n",
"$$"
]
},
@@ -778,6 +778,7 @@
"We will amongst other things show that the regularization parameter can reduce considerably the variance of the parameters $\\beta$.\n",
"\n",
"\n",
"\n",
"<!-- !split -->\n",
"## Linking the regression analysis with a statistical interpretation\n",
"\n",