Bounded Influence Regression in the Presence of Heteroskedasticity of Unknown Form

In a regression model with conditional heteroskedasticity of unknown form, we propose a general class of M-estimators scaled by nonparametric estimates of the conditional standard deviations of the dependent variable. We give regularity conditions under which these estimators are asymptotically equivalent to M-estimators scaled by the true conditional standard deviations. The practical performance of these estimators is investigated through a Monte Carlo experiment

PCB exposure and cochlear function at age 6 years

Epidemiological studies have documented adverse associations between exposure to polychlorinated biphenyls (PCBs) and otological outcomes. Previously, we documented decreased distortion product otoacoustic emission (DPOAE) levels in children exposed to PCBs, up to the age of 45 months, amongst a cohort of children in eastern Slovakia. The objective of the present study is to evaluate cochlear dysfunction at 72 months of age in 214 children from this same cohort and to compare the otoacoustic test sensitivity to that of pure tone audiometry (PTA). The association between DPOAE, PTA, and PCBs was estimated by means of multivariate ANOVA (MANOVA) and linear regression models. ROC curves were computed to estimate the DPOAE-test power in children. The DPOAE level at 72 months was related to PCB-153 serum levels. The DPOAE Input/Output function test at mid-frequency (2kHz) has shown instead nonmonotonic dependence on PCB exposure, for the left ears of children, over the whole growth curve. No significant association was found between PTA hearing levels and PCB-153 concentration. High diagnostic power of the DPOAE-test was found in children, similar to that found by the same authors in adults. In conclusions the DPOAE-PCB correlation obtained at 72 months is similar to that at 45 months suggesting a permanent and stable ototoxic effect of the PCB exposure. The lack of statistical significance of the PCB-PTA correlation suggests that DPOAEs are sensitive biomarkers of cochlear damage