Comparison of Prediction Methods When Only a Few Components are Relevant
研究了在解释变量较多且只有少数成分与因变量相关时，四种预测方法的比较，发现主成分回归和偏最小二乘回归在不同特征值条件下各有优势，而一种最大似然型方法在渐近意义上表现最优。
Abstract We consider prediction in a multiple regression model where we also look on the explanatory variables as random. If the number of explanatory variables is large, then the common least squares multiple regression solution may not be the best one. We give a methodology for comparing certain alternative prediction methods by asymptotic calculations and perform such a comparisons for four specific methods. The results indicate that none of these methods dominates the others, and that the difference between the methods typically (but not always) is small when the number of observations is large. In particular, principal component regression does well when the eigenvalues corresponding to components not correlated with the dependent variables (i.e., the irrelevant eigenvalues) are extremely small or extremely large. Partial least squares regression does well for intermediate irrelevant eigenvalues. A maximum likelihood-type method dominates the others asymptotically, at least in the case of one relevant component.