Partial Linear Model
It is popular to summarize the relationship between an outcome variable y and a vector (x, z) through a linear mean regression where the mean of y is modelled as a linear function of both x and z. A more robust specification is called for in some situations where the imposed linear relationship between (the mean of) y and z is suspect. A partially linear specification allows for a regression function that maintains linearity in x but allows the effect of z to be nonlinear. This partially linear model has been widely studied in the statistics and the semiparametric econometrics literature.
KeywordsAge elasticity Bootstrap Censored selection models Conditional expectations Convergence Cross validation Heteroskedasticity Homoskedasticity Income elasticity Kernel estimators Linear models Linear regression Nonparametric estimation Nonparametric selection models Partially linear models Quantile regression Random variables Semiparametric estimation Semiparametric sieve least squares Sieves Spline regression
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