Lecture9 - Lecture 9 Modern Regression Suppose that we...

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Lecture 9. Modern Regression Suppose that we consider a multiple linear regression model Y = β 0 + p X j =1 β j X j + ε, j = 1 , 2 , . . . , p (8.1) The relationship between Y and regressors X j is frequently to be described by non-trivial non-linear functions. The Alternative Conditional Expectation (ACE) algorithm smoothly transforms X j in order to maximize the correlation between the response and the transformed predictors. In particular, the model defined by (8.1) may be replaced by the linear additive model Y = α + p X j =1 f j ( X j ) + ε, j = 1 , 2 , 3 . (8.2) Here f j are some smooth non-linear functions. Since f j is rather general, the new model 8.2 obviously subsumes the old model 8.1. The overall goal of ACE is to ”linearize” the relationship between the predictand Y and predictors X j . In particular, ACE finds transformations of predictors, f j , that make the re- lationship between Y and ”new” transformed predictors f j ( X j ) as linear as possible and automatically selects such smooth functions f j
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