7 problems

Let $psi\to z(psi)$ be the PLS-related mapping, and let $mathcal{C}z=lbrace psi otinmathbb{R}+^mbigm|V^T Zpsi=0rbrace$ be the associated polyhedral cone. Write its extremal rays as…

Let a PLS estimator use a specified number of PLS directions, and let its degrees of freedom be denoted by DoF. PLS degrees-of-freedom conjecture. The degrees of freedom of PLS alw…

The article studies the partial least-squares estimator $\widehat{\bm{\beta}}_a$ and conditions under which it has better mean-square prediction performance than an arbitrary estim…

Let $J\geq0$ be the number of sample IRPLS iterations, let $c>0$ be a possibly small constant, and let $J_{0}\geq0$ depend on the distribution of the latent model. Suppose the clas…

Consider the generalized-linear-model extension with sample IRPLS estimator $\widehat{\boldsymbol{\beta}}_{\widehat{s}}^{(J)}$, where $J\geq0$ is fixed, and let…

Sample PLS asymptotic normality conjecture. The sample PLS is asymptotically normal with

Let $m$ denote the number of components in a partial least squares regression fit, and let $\operatorname{DoF}(m)$ denote its degrees of freedom. Degrees-of-freedom lower-bound con…