Gaussian least-squares contrast
= Gaussian least-squares contrast
{c}
Because Gaussian white noise is not an $\ell^2$ vector, least squares over $\Theta\subset\ell^2$ is defined by maximizing
$$
2\langle Y,\theta\rangle-\lVert\theta\rVert_2^2
$$
over $\theta\in\Theta$, with the noise pairing interpreted through an <isonormal Gaussian process>. Differences of this contrast equal the formal differences of squared residual norms.