Ridge estimator in singulah oesiun with application to age-period-cohort analysis of disease rates

Abstract

Ridge estimator of a singular design is considered for linear and gener¬alized linear models. Ridge penalty helps determine a unique estimator in singmar uesign. me tuning parameter o± tue penalty is seiecteu via gener¬alized cross-validation (GCV) method. It is proven that the ridge estimator lies in a special sub-parameter space and converges to the intrinsic estimator, an estimable function in singular design, as the shrinkage penalty diminishes. The expansion of the ridge estimator and its variance are also obtained. Thismethod is demonstrated through an application to age-period-cohort (APC) analysis of the incidence rates of cervical cancer in Ontario women 1980-1994