Linear source invertible bimodules and Green correspondence

Prediction in invertible linear processes

We construct root-n consistent plug-in estimators for conditional expectations of the form E(h(Xn+1, . . . , Xn+m)|X1, . . . , Xn) in invertible linear processes. More specifically, we prove a Bahadur type representation for such estimators, uniformly over certain classes of not necessarily bounded functions h. We obtain in particular a uniformly root-n consistent estimator for the m-dimensiona...

Efficient Estimation in Invertible Linear Processes

Taylor expansion in linear logic is invertible

Each Multiplicative Exponential Linear Logic (MELL) proof-net can be expanded into a differential net, which is its Taylor expansion. We prove that two different MELL proof-nets have two different Taylor expansions. As a corollary, we prove a completeness result for MELL: We show that the relational model is injective for MELL proof-nets, i.e. the equality between MELL proof-nets in the relatio...

Invertible Piecewise Linear Approximations for Color Reproduction

We consider the use of linear splines with variable knots for the approximation of unknown functions from data , motivated by control and estimation problems arising in color systems management. Unlike most popular nonlinear-in-parameters representations, piecewise linear (PL) functions can be simply inverted in closed form. For the one-dimensional case, we present a study comparing P L and neu...

Improved Density Estimators for Invertible Linear Processes

ABSTRACT The stationary density of a centered invertible linear processes can be represented as a convolution of innovation-based densities, and it can be estimated at the parametric rate by plugging residual-based kernel estimators into the convolution representation. We have shown elsewhere that a functional central limit theorem holds both in the space of continuous functions vanishing at in...