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We propose a generalized partially linear functional single index risk scoremodel for repeatedly measured outcomes where the index itself is a function oftime. We fuse the nonparametric kernel method and regression spline method, andmodify the generalized estimating equation to facilitate estimation andinference. We use local smoothing kernel to estimate the unspecifiedcoefficient functions of time, and use B-splines to estimate the unspecifiedfunction of the single index component. The covariance structure is taken intoaccount via a working model, which provides valid estimation and inferenceprocedure whether or not it captures the true covariance. The estimation methodis applicable to both continuous and discrete outcomes. We derive large sampleproperties of the estimation procedure and show a different convergence ratefor each component of the model. The asymptotic properties when the kernel andregression spline methods are combined in a nested fashion has not been studiedprior to this work, even in the independent data case.

Fused kernel-spline smoothing for repeatedly measured outcomes in a generalized partially linear model with functional single index