Optimal detection of liquid ionization calorimeter signal in experimental particle physics is considered. A few linear and nonlinear approaches for amplitude and arrival time estimation based on the χ² function are compared in simulation considering the noise sample correlation introduced by the analog pulse shaper. The estimation bias of the first-order approximation, a.k.a linear optimal filtering, is studied and contrasted to those of the second-order as well as the exhaustive search. A gradient-descent technique is presented as an alternative to the exhaustive search with significantly reduced search time and computation complexity. Results from various pulse shapers including the CR-RC², CR-RC³, and CR²-RC² are also compared.