CHOOSING THE NUMBER OF REPETITIONS IN THE MULTIPLE PLUG-IN OPTIMIZATION METHOD FOR THE RIDGE PARAMETERS IN MULTIVARIATE GENERALIZED RIDGE REGRESSION

Multivariate generalized ridge (MGR) regression was proposed by Yanagihara, Nagai, and Satoh (2009) in order to avoid the multicollinearity problem in multivariate linear regression models. The MGR estimator is defined by using multiple nonnegative ridge parameters in an ordinary least-squares (LS) estimator. In order to optimize these ridge parameters, Yanagihara, Nagai, and Satoh (2009) and Nagai, Yanagihara, and Satoh (2012) proposed several optimization methods. We focus on the plugin optimization method, which is an estimation method for the principal optimal ridge parameters that minimizes the predicted mean squared error. The plug-in optimization method is a repeating method that uses the current ridge parameters estimate as input in order to obtain an improved estimate. In the present paper, we propose two criteria for choosing the number of repetitions. We conducted several numerical studies using the proposed information criterion to compare the LS and MGR estimators with the optimized ridge parameters based on some ordinary plug-in optimization methods, and those obtained by using the optimized multiple plug-in optimization method.