🤖 AI Summary
This study addresses the challenges of overfitting induced by basis function expansion and penalty parameter selection in nonparametric GMANOVA models. To this end, a plug-in optimization approach is introduced into the generalized ridge regression estimation framework. By extending this specific plug-in method to the nonparametric GMANOVA setting for the first time, the proposed approach enables efficient computation of penalty parameters and simplifies the algorithm, significantly reducing iterative computational costs. Numerical experiments demonstrate that the method effectively mitigates overfitting and enhances estimation stability. Overall, this work provides a novel avenue for nonparametric multivariate analysis that combines theoretical rigor with computational efficiency.
📝 Abstract
In order to estimate the longitudinal trend, we often use the generalized multivariate analysis of variance (GMANOVA) model (Potthoff \& Roy, 1964), when the longitudinal data is balanced data. Usually, we use this GMANOVA model with some polynomial at the time of measurement. However, when the longitudinal trend has flexible curve, we cannot derive good fitting estimated curve when we use some polynomial curves. Then, Nagai (2011) proposed the nonparametric GMANOVA model which uses on several known basis functions instead of using the polynomial curves. If we use several basis functions, then overfitting problem is occurred. Nagai (2011) also proposed the estimation method for avoiding overfitting and unstable problems, and reducing computational iterative algorithm by extending the generalized ridge regression model (Yanagihara, Nagai \& Satoh, 2009). In the present paper, we extend one of the optimization methods in Nagai, Yanagihara and Satoh (2012) into the estimation method in Nagai (2011). Through numerical studies, we show some properties of each optimization method.