A study of sensitivity analysis on the method of principal Hessian directions
A nonlinear dimension reduction problem is considered with data described by the model \(y_j=g(\beta'_1x_j,\dots,\beta_k'x_j,\varepsilon_j)\), where \((y_j,x_j)_{j=1}^n\) are observations, \(g:R^k\to R\) is an unknown function, \(\beta_i\) are unknown and should be estimated, and \(\varepsilon_j\) is a random error. The principal Hessian directions (PHD) technique is described for estimation of the \(\beta_j\). Then the case is considered where \(k=2\), \(\varepsilon_j\) are absent, but \(y\) and \(x\) can be perturbed at some points by an additive Gaussian noise. For this case the asymptotic distribution of the angle between the perturbed and non-perturbed PHD is described. Results of simulations and analysis of base ball data are presented.
scientific article; zbMATH DE number 1878602