(V &lt; U | U &gt; u, V &gt; u)\) and
\(\varphi_0(u) = \Pr(V = U | U &gt; u, V &gt; u)\)
Define
$$ \varphi(u) = \frac{\varphi_{+} - \varphi_{-}}{\varphi_{+} + \varphi_{-}}$$</p>
<p>The empirical likelihood estimator, derived for max-stable vectors with unit Frechet margins, is
$$\frac{\sum_i p_i I(w_i \leq 0.5) - 0.5}{0.5 - 2\sum_i p_i(0.5-w_i) I(w_i \leq 0.5)}$$
where \(p_i\) is the empirical likelihood weight for observation \(i\) and \(w_i\) is the pseudo-angle associated to the first coordinate.</p>
   