The distribution of Pearson residuals in generalized linear models

In general, the distribution of residuals cannot be obtained explicitly. We give an asymptotic formula for the density of Pearson residuals in continuous generalized linear models corrected to order $n^{-1}$, where $n$ is the sample size. We define corrected Pearson residuals for these models that, to this order of approximation, have exactly the same distribution of the true Pearson residuals. Applications for important generalized linear models are provided and simulation results for a gamma model illustrate the usefulness of the corrected Pearson residuals

Minimalist Approach for the Design of Microstructured Optical Fiber Sensors

We report on recent investigations regarding ultra-simplified designs for microstructured optical fiber sensors. This minimalist approach relies on the utilization of capillary-like fibers—namely embedded-core fibers, surface-core fibers, and capillary fibers—as platforms for the realization of sensing measurements. In these fibers, guidance of light is accomplished in an embedded or surface germanium-doped core or in the hollow part of capillaries. External stimuli can alter fiber wall thickness and/or induce birefringence variations, allowing, for the embedded-core and capillary fibers, to operate as pressure or temperature sensors. For the surface-core fiber design, the interaction between the guided mode and external medium allows the realization of refractive index sensing either by using fiber Bragg gratings or surface plasmon resonance phenomenon. Also, we report the realization of directional curvature sensing with surface-core fibers making use of the off-center core position. The attained sensitivities are comparable to the ones obtained with much more sophisticated structures. The results demonstrate that these novel geometries enable a new route toward the simplification of optical fiber sensors