Ridge estimator in singular design with application to age-period-cohort analysis of disease rates

Ridge estimator of a singular design is considered for linear and generalized linear models. Ridge penalty helps determine a unique estimator in singular design. The tuning parameter of the penalty is selected via generalized 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. This method is demonstrated through an application to age-period-cohort (APC) analysis of the incidence rates of cervical cancer in Ontario women 1960-1994.