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Empirical Likelihood emplike
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<h1 id="empirical-likelihood-emplike"><span id="emplike"></span>Empirical Likelihood <code class="xref py py-mod docutils literal notranslate"><span class="pre">emplike</span></code><a class="headerlink" href="#empirical-likelihood-emplike" title="Link to this heading">¶</a></h1>
<h2 id="introduction">Introduction<a class="headerlink" href="#introduction" title="Link to this heading">¶</a></h2>
<p>Empirical likelihood is a method of nonparametric inference and estimation that lifts the
obligation of having to specify a family of underlying distributions. Moreover, empirical
likelihood methods do not require re-sampling but still
uniquely determine confidence regions whose shape mirrors the shape of the data.
In essence, empirical likelihood attempts to combine the benefits of parametric
and nonparametric methods while limiting their shortcomings. The main difficulties of
empirical likelihood is the computationally intensive methods required to conduct inference.
<a class="reference internal" href="#module-statsmodels.emplike" title="statsmodels.emplike: Empirical likelihood tools"><code class="xref py py-mod docutils literal notranslate"><span class="pre">statsmodels.emplike</span></code></a> attempts to provide a user-friendly interface that allows the
end user to effectively conduct empirical likelihood analysis without having to concern
themselves with the computational burdens.</p>
<p>Currently, <code class="xref py py-mod docutils literal notranslate"><span class="pre">emplike</span></code> provides methods to conduct hypothesis tests and form confidence
intervals for descriptive statistics. Empirical likelihood estimation and inference
in a regression, accelerated failure time and instrumental variable model are
currently under development.</p>
<h3 id="references">References<a class="headerlink" href="#references" title="Link to this heading">¶</a></h3>
<p>The main reference for empirical likelihood is:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><code><span class="n">Owen</span><span class="p">,</span> <span class="n">A</span><span class="o">.</span><span class="n">B</span><span class="o">.</span> <span class="s2">"Empirical Likelihood."</span> <span class="n">Chapman</span> <span class="ow">and</span> <span class="n">Hall</span><span class="p">,</span> <span class="mf">2001.</span>
</code></pre></div>
</div>
<h2 id="examples">Examples<a class="headerlink" href="#examples" title="Link to this heading">¶</a></h2>
<div class="highlight-ipython notranslate"><div class="highlight"><pre><span></span><code><span class="gp">In [1]: </span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="gp">In [2]: </span><span class="kn">import</span><span class="w"> </span><span class="nn">statsmodels.api</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">sm</span>
<span class="go"># Generate Data</span>
<span class="gp">In [3]: </span><span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">standard_normal</span><span class="p">(</span><span class="mi">50</span><span class="p">)</span>
<span class="go"># initiate EL</span>
<span class="gp">In [4]: </span><span class="n">el</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">emplike</span><span class="o">.</span><span class="n">DescStat</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="go"># confidence interval for the mean</span>
<span class="gp">In [5]: </span><span class="n">el</span><span class="o">.</span><span class="n">ci_mean</span><span class="p">()</span>
<span class="gh">Out[5]: </span><span class="go">(np.float64(-0.2315025722371276), np.float64(0.263034787369957))</span>
<span class="go"># test variance is 1</span>
<span class="gp">In [6]: </span><span class="n">el</span><span class="o">.</span><span class="n">test_var</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<span class="gh">Out[6]: </span><span class="go">(np.float64(2.4596243120706216), np.float64(0.11680671686076974))</span>
</code></pre></div>
</div>
<h2 id="module-statsmodels.emplike"><span id="module-reference"></span>Module Reference<a class="headerlink" href="#module-statsmodels.emplike" title="Link to this heading">¶</a></h2>
<table class="autosummary longtable docutils data align-default">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.emplike.descriptive.DescStat.html#statsmodels.emplike.descriptive.DescStat" title="statsmodels.emplike.descriptive.DescStat (Python function) — Returns an instance to conduct inference on descriptive statistics via empirical likelihood. See DescStatUV and DescStatMV for more information."><code class="xref py py-obj docutils literal notranslate"><span class="pre">descriptive.DescStat</span></code></a>(endog)</p></td>
<td><p>Returns an instance to conduct inference on descriptive statistics via empirical likelihood.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/statsmodels.emplike.descriptive.DescStatUV.html#statsmodels.emplike.descriptive.DescStatUV" title="statsmodels.emplike.descriptive.DescStatUV (Python class) — A class to compute confidence intervals and hypothesis tests involving mean, variance, kurtosis and skewness of a univariate random variable."><code class="xref py py-obj docutils literal notranslate"><span class="pre">descriptive.DescStatUV</span></code></a>(endog)</p></td>
<td><p>A class to compute confidence intervals and hypothesis tests involving mean, variance, kurtosis and skewness of a univariate random variable.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.emplike.descriptive.DescStatMV.html#statsmodels.emplike.descriptive.DescStatMV" title="statsmodels.emplike.descriptive.DescStatMV (Python class) — A class for conducting inference on multivariate means and correlation."><code class="xref py py-obj docutils literal notranslate"><span class="pre">descriptive.DescStatMV</span></code></a>(endog)</p></td>
<td><p>A class for conducting inference on multivariate means and correlation.</p></td>
</tr>
</tbody>
</table>
<hr>
<div class="md-source-file">
<small>