Part of the Springer Series in Statistics book series (SSS)
Generalized Partial Linear Models
As indicated in the overview in Chapter 5, a partial linear model (PLM) consists of two additive components, a linear and a nonparametric part:
where β=(β1,...,β p )is a finite dimensional parameter and m(●) a smooth function. Here, we assume again a decomposition of the explanatory variables into two vectors, U and T. The vector U denotes a p-variate random vector which typically covers categorical explanatory variables or variables that are known to influence the index in a linear way. The vector T is a q-variate random vector of continuous explanatory variables which is to be modeled in a nonparametric way. Economic theory or intuition should guide you as to which regressors should be included in U or T, respectively.
$$ E(Y|U,T) = U^ \top \beta + m(T) $$
KeywordsEstimation Algorithm Nonparametric Function Semiparametric Estimate Partial Linear Model Parametric Part
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© Springer-Verlag Berlin Heidelberg 2004