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We present an extension to the conventional transition mean model by adding a conditional variance model and assuming unknown link and variance functions. This extension gives rise to great flexibility of addressing not only the transitional relationship between the response and covariates but also the heteroscedastic mechanism of the underlying measurement process. We propose a kernel-based nonparametric estimation and inference for the regression parameters. Our estimation procedure for the regression coefficients detours the unknown link and variance functions, and hence its implementation is rather straightforward. The simulation studies show that the proposed methodology is particularly useful to extract the mean signals when they are heavily masked by strong variation. Both root-n parametric rate consistency and asymptotic normality of the proposed estimators are established. Numerical illustrations include also an analysis of longitudinal data on the length of women’s menstrual cycles.

Longitudinal semiparametric transition models with unknown link and variance functions