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pseudo_obs.html
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pseudo_obs.html
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<title>Pseudo-Observations — pseudo_obs • rvinecopulib</title>
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<h1>Pseudo-Observations</h1>
<small class="dont-index">Source: <a href='https://github.com/vinecopulib/rvinecopulib/blob/master/R/tools.R'><code>R/tools.R</code></a></small>
<div class="hidden name"><code>pseudo_obs.Rd</code></div>
</div>
<div class="ref-description">
<p>Compute the pseudo-observations for the given data matrix.</p>
</div>
<pre class="usage"><span class='fu'>pseudo_obs</span><span class='op'>(</span><span class='va'>x</span>, ties_method <span class='op'>=</span> <span class='st'>"average"</span>, lower_tail <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span></pre>
<h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
<table class="ref-arguments">
<colgroup><col class="name" /><col class="desc" /></colgroup>
<tr>
<th>x</th>
<td><p>vector or matrix random variates to be converted (column wise) to
pseudo-observations.</p></td>
</tr>
<tr>
<th>ties_method</th>
<td><p>similar to <code>ties.method</code> of <code><a href='https://rdrr.io/r/base/rank.html'>rank()</a></code> (only <code>"average"</code>,
<code>"first"</code> and <code>"random"</code> currently available).</p></td>
</tr>
<tr>
<th>lower_tail</th>
<td><p><code>logical</code> which, if `FALSE``, returns the
pseudo-observations when applying the empirical marginal survival
functions.</p></td>
</tr>
</table>
<h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
<p>a vector of matrix of the same dimension as the input containing the
pseudo-observations.</p>
<h2 class="hasAnchor" id="details"><a class="anchor" href="#details"></a>Details</h2>
<p>Given <code>n</code> realizations \(x_i=(x_{i1}, \ldots,x_{id})\),
\(i \in \left\lbrace 1, \ldots,n \right\rbrace \)
of a random vector <code>X</code>, the pseudo-observations are defined via
\(u_{ij}=r_{ij}/(n+1)\) for
\(i \in \left\lbrace 1, \ldots,n \right\rbrace\)
and
\(j \in \left\lbrace 1, \ldots,d \right\rbrace \), where
\(r_{ij}\) denotes the rank of \(x_{ij}\) among all \(x_{kj}\),
\(k \in \left\lbrace 1, \ldots,n \right\rbrace \).</p>
<p>The pseudo-observations can thus also be computed by component-wise applying
the empirical distribution functions to the data and scaling the result by
\(n/(n+1)\). This asymptotically negligible scaling factor is used to force
the variates to fall inside the open unit hypercube, for example, to avoid
problems with density evaluation at the boundaries.</p>
<p>When <code>lower_tail = FALSE</code>, then <code>pseudo_obs()</code> simply returns
<code>1 - pseudo_obs()</code>.</p>
<h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
<pre class="examples"><div class='input'><span class='co'># pseudo-observations for a vector</span>
<span class='fu'>pseudo_obs</span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/stats/Normal.html'>rnorm</a></span><span class='op'>(</span><span class='fl'>10</span><span class='op'>)</span><span class='op'>)</span>
</div><div class='output co'>#> [1] 0.72727273 0.81818182 0.54545455 0.63636364 0.90909091 0.27272727
#> [7] 0.36363636 0.45454545 0.09090909 0.18181818</div><div class='input'>
<span class='co'># pseudo-observations for a matrix</span>
<span class='fu'>pseudo_obs</span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/cbind.html'>cbind</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/stats/Normal.html'>rnorm</a></span><span class='op'>(</span><span class='fl'>10</span><span class='op'>)</span>, <span class='fu'><a href='https://rdrr.io/r/stats/Normal.html'>rnorm</a></span><span class='op'>(</span><span class='fl'>10</span><span class='op'>)</span><span class='op'>)</span><span class='op'>)</span>
</div><div class='output co'>#> [,1] [,2]
#> [1,] 0.90909091 0.27272727
#> [2,] 0.54545455 0.63636364
#> [3,] 0.36363636 0.45454545
#> [4,] 0.18181818 0.18181818
#> [5,] 0.09090909 0.09090909
#> [6,] 0.45454545 0.54545455
#> [7,] 0.81818182 0.90909091
#> [8,] 0.63636364 0.72727273
#> [9,] 0.27272727 0.36363636
#> [10,] 0.72727273 0.81818182</div></pre>
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