Updating least squares
Likelihood-based procedures are a common way to estimate tail dependence parameters.They are not applicable, however, in non-differentiable models such as those arising from recent max-linear structural equation models.The mainstay in our presented algorithm for the solution of LSE problem is the updating procedure.Therefore, our main concern is to study the error analysis of the updating steps.
In large samples, it is asymptotically normal with an explicit and estimable covariance matrix.Moreover, they can be hard to compute in higher dimensions.An adaptive weighted least-squares procedure matching nonparametric estimates of the stable tail dependence function with the corresponding values of a parametrically specified proposal yields a novel minimum-distance estimator.It is useful in applications such as in solving a sequence of modified related problems by adding or removing data from the original problem.Stable and efficient methods of updating are required in various fields of science and engineering such as in optimization and signal processing [In this section, we will study the backward stability of our proposed Algorithm 5.
Allows positive "damping".) lusol Z: MATLAB software for computing a nullspace operator \(Z\) of the transpose of a sparse matrix \(S\) (so that \(S^T Z = 0\)) using sparse QR factors of either \(S\) or \(S^T\) computed by Suite Sparse QR, or sparse LU factors of either \(S\) or \(S^T\) computed by LUSOL.