mhjensen
267 lines
13 KiB
HTML
267 lines
13 KiB
HTML
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<title>Week 36: Resampling techniques and Ordinary Least Square</title>
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'sections': [('Plans for week 36', 2, None, '___sec0'),
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('Thursday September 3', 2, None, '___sec1'),
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('Why resampling methods', 2, None, '___sec2'),
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('Resampling methods', 2, None, '___sec3'),
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('Resampling approaches can be computationally expensive',
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('Why resampling methods ?', 2, None, '___sec5'),
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('Resampling methods', 2, None, '___sec11'),
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('Resampling methods: Jackknife', 2, None, '___sec13'),
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('Code example for the Bootstrap method', 2, None, '___sec20'),
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('Various steps in cross-validation', 2, None, '___sec21'),
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('How to set up the cross-validation for Ridge and/or Lasso',
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('The bias-variance tradeoff', 2, None, '___sec25'),
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('Understanding what happens', 2, None, '___sec27'),
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("Another Example from Scikit-Learn's Repository",
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<a class="navbar-brand" href="week36-bs.html">Week 36: Resampling techniques and Ordinary Least Square</a>
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._week36-bs001.html#___sec0" style="font-size: 80%;">Plans for week 36</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs002.html#___sec1" style="font-size: 80%;">Thursday September 3</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs003.html#___sec2" style="font-size: 80%;">Why resampling methods</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs004.html#___sec3" style="font-size: 80%;">Resampling methods</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs005.html#___sec4" style="font-size: 80%;">Resampling approaches can be computationally expensive</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs006.html#___sec5" style="font-size: 80%;">Why resampling methods ?</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs007.html#___sec6" style="font-size: 80%;">Statistical analysis</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs008.html#___sec7" style="font-size: 80%;">Linking the regression analysis with a statistical interpretation</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs009.html#___sec8" style="font-size: 80%;">Assumptions made</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs010.html#___sec9" style="font-size: 80%;">Expectation value and variance</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs011.html#___sec10" style="font-size: 80%;">Expectation value and variance for \( \boldsymbol{\beta} \)</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs012.html#___sec11" style="font-size: 80%;">Resampling methods</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs013.html#___sec12" style="font-size: 80%;">Resampling methods: Jackknife and Bootstrap</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs014.html#___sec13" style="font-size: 80%;">Resampling methods: Jackknife</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs015.html#___sec14" style="font-size: 80%;">Jackknife code example</a></li>
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<!-- navigation toc: --> <li><a href="#___sec15" style="font-size: 80%;">Resampling methods: Bootstrap</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs017.html#___sec16" style="font-size: 80%;">Resampling methods: Bootstrap background</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs018.html#___sec17" style="font-size: 80%;">Resampling methods: More Bootstrap background</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs019.html#___sec18" style="font-size: 80%;">Resampling methods: Bootstrap approach</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs020.html#___sec19" style="font-size: 80%;">Resampling methods: Bootstrap steps</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs021.html#___sec20" style="font-size: 80%;">Code example for the Bootstrap method</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs022.html#___sec21" style="font-size: 80%;">Various steps in cross-validation</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs023.html#___sec22" style="font-size: 80%;">How to set up the cross-validation for Ridge and/or Lasso</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs024.html#___sec23" style="font-size: 80%;">Cross-validation in brief</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs025.html#___sec24" style="font-size: 80%;">Code Example for Cross-validation and \( k \)-fold Cross-validation</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs026.html#___sec25" style="font-size: 80%;">The bias-variance tradeoff</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs027.html#___sec26" style="font-size: 80%;">Example code for Bias-Variance tradeoff</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs028.html#___sec27" style="font-size: 80%;">Understanding what happens</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs029.html#___sec28" style="font-size: 80%;">Summing up</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs030.html#___sec29" style="font-size: 80%;">Another Example from Scikit-Learn's Repository</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs031.html#___sec30" style="font-size: 80%;">More examples on bootstrap and cross-validation and errors</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs032.html#___sec31" style="font-size: 80%;">The same example but now with cross-validation</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs033.html#___sec32" style="font-size: 80%;">Cross-validation with Ridge</a></li>
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<!-- navigation toc: --> <li><a href="._week36-bs034.html#___sec33" style="font-size: 80%;">Friday September 4</a></li>
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<p> </p><p> </p><p> </p> <!-- add vertical space -->
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<a name="part0016"></a>
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<!-- !split -->
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<h2 id="___sec15" class="anchor">Resampling methods: Bootstrap </h2>
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<div class="panel panel-default">
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<div class="panel-body">
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<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
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Bootstrapping is a nonparametric approach to statistical inference
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that substitutes computation for more traditional distributional
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assumptions and asymptotic results. Bootstrapping offers a number of
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advantages:
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<ol>
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<li> The bootstrap is quite general, although there are some cases in which it fails.</li>
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<li> Because it does not require distributional assumptions (such as normally distributed errors), the bootstrap can provide more accurate inferences when the data are not well behaved or when the sample size is small.</li>
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<li> It is possible to apply the bootstrap to statistics with sampling distributions that are difficult to derive, even asymptotically.</li>
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<li> It is relatively simple to apply the bootstrap to complex data-collection plans (such as stratified and clustered samples).</li>
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</ol>
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</div>
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</div>
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<p>
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