Semiparametric Efficiency in Longitudinal Marginal Models

Raymond J. Carroll
Texas A&M University

We consider the marginal longitudinal model in which repeated measures
are taken on each individual. The model is in partially linear form m(X)
+ Zb up to a link function, and interest is in estimating the regression
parameter b. Profile kernel methods are developed to estimate b: these
methods have the feature that each smoothing step can be performed with
bandwidths that are of the usual rate. The methods are shown to be
semiarametric efficient in the Gaussian model. We contrast our methods
with the standard device of working independence, and show that
considerable gains in efficiency are possible. The same results are
shown to hold in the Gaussian case when smoothing splines are the
nonparametric driver: this requires that we derive the bias and variance
expressions for smoothing splines in independent and correlated data.