torch_openreml.blue

torch_openreml.blue(y, x, v)

Compute the best linear unbiased estimator (BLUE) of the fixed effects.

Solves for \(\hat{\boldsymbol{\beta}}\) via generalised least squares:

\[\hat{\boldsymbol{\beta}} = (\symbf{X}^\top \symbf{V}^{-1} \symbf{X})^{-1} \symbf{X}^\top \symbf{V}^{-1} \symbf{y}\]

Parameters:

• y (torch.Tensor) – Response vector of shape (n,).

• x (torch.Tensor) – Fixed-effect design matrix of shape (n, p).

• v (torch.Tensor) – Marginal covariance matrix of shape (n, n), e.g. \(\symbf{V}(\boldsymbol{\theta})\) evaluated at fitted covariance parameters.

Returns:

Coefficient estimate \(\hat{\boldsymbol{\beta}}\)

of shape (p,).

Return type:

torch.Tensor