function lambda_opt(x)

    n = size(x, 1)
    wmean_2 = (x' * x).^2
    x2 = x.^2
    x2 = (x2' * x2)

    diag_idx = diagind(wmean_2)

    first_eq = x2 .-(wmean_2./n)
    second_eq = (n / (n - 1)^3)

    m_temp = first_eq * second_eq
    var_w  = sum(m_temp) - sum(m_temp[diag_idx])

    s2_temp = wmean_2
    s2_temp2 = wmean_2[diag_idx]
    s2 = sum(s2_temp / (n - 1)^2) - sum(s2_temp2 / (n - 1)^2)

    lambda = max(0 , min(var_w / s2, 1))

end