Co. Wu et al., Asymptotic confidence regions for kernel smoothing of a varying-coefficient model with longitudinal data, J AM STAT A, 93(444), 1998, pp. 1388-1402
We consider the estimation of the k + 1-dimensional nonparametric component
beta(t) of the varying-coefficient model Y(t) = X-T(t)beta(t) + epsilon(t)
based on longitudinal observations (Y-ij, X-i(t(ij)), t(ij)), i = 1,..., n
,j = i,..., n(i), where t(ij) is the jth observed design time point t of th
e ith subject and Y-ij and X-i(t(ij)) are the real-valued outcome and Rk+1
valued covariate vectors of the ith subject at t(ij). The subjects are inde
pendently selected, but the repeated measurements within subject are possib
ly correlated. Asymptotic distributions are established for a kernel estima
te of beta(t) that minimizes a local least squares criterion. These asympto
tic distributions are used to construct a class of approximate pointwise an
d simultaneous confidence regions for beta(t). Applying these methods to an
epidemiological study, we show that our procedures are useful for predicti
ng CD4 (T-helper lymphocytes) cell changes among HIV (human immunodeficienc
y virus)-infected persons. The finite-sample properties of our procedures a
re studied through Monte Carlo simulations.