FUZZY SEMIPARAMETRIC PARTIAL LINEAR MODELS BASED ON RIDGE ESTIMATION

Multicollinearity may lead to unstable least-squares coefficients and introduce errors in the smooth part of a fuzzy semiparametric partial linear model. This paper introduces a ridge estimator for five linear meteorological effects and models wind speed nonparametrically under LR fuzzy responses. A Diamond-distance residual criterion is combined with a quadratic penalty, and a two-stage procedure is applied to 21 daily fuzzy carbon-monoxide observations formed from hourly measurements in Rome. The six inputs are standard-centred; the reported fit uses a Gaussian kernel with bandwidth 0.08 and a ridge parameter of 0.1. Ridge fitting reduces MSEe from 0.0763 to 0.0508 and MAPEe from 2.4003% to 1.6370% compared with ordinary two-step estimation. It also improves on the reported fuzzy linear comparator for these measures, although that model uses a different predictor subset and preprocessing. The case shows how ridge shrinkage can stabilise the parametric part without affecting the smooth term.