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How to find vertices of intersection of two hyperplanes?
According to Shapiro and Wilk(1965) in lemma 3,
$W$ has lower bound: $na_1^2/(n-1).$
To find this value, they solve the problem:
$$Max\quad y'y$$
$$ s.t.\quad 1'y=0,\quad and\quad a'y = 1,\quad and \...
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$\max_{\{X_N\}}{\frac{\mu^2(X_N)}{\mu^2(X_N)+\sigma^2(X_N)}}$ for $X_N=\{x_1,...,x_n\},x_i\in \mathbb{N}^+,\exists(i,j):x_i\neq x_j$
Short version of the question
Consider
\begin{equation}
g(X_n)=\frac{\mu^2(X_N)}{\mu^2(X_N)+\sigma^2(X_N)}\\
X_N=\{x_1,x_2,...,x_n\},n>1,\forall i:x_i\in \mathbb{N}^+,\exists(i,j):x_i\neq x_j
\end{...
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