1. Row-wise cross-validation $$ \begin{aligned} CV(k) &= \sum_{i=1}^N \lvert \lvert \mathbf{x}_i - \boldsymbol{\xi} \boldsymbol{f}i^T \lvert\vert^2 \ &= \sum{i=1}^N \lvert \lvert \mathbf{x}_i - \boldsymbol{\xi} (\mathbf{x}_i^T\boldsymbol{\xi})^T \lvert\vert^2 \end{aligned} $$ where $\boldsymbol\xi$ is a PC function(PC loading) with $k$ eigenvectors and $\boldsymbol{f}_i$ is $i$th PC score with $k$ components. $\mathbf{x}_i$를 predict하는
Outline Introduction The Growth Curve Data The Reduced Rank Model Fitting the Reduced Rank Model The Reduced Rank and Mixed Effects Methods Compared Model Selection and Inference Comparison of the Reduced Rank Method and Classical Principal Components Appendix 1. Introduction The problem If each curves observed different time points, it is not good way to apply method with equal time points. In this paper, present an estimation technique when the