Abstract

Let X(t), t in [a,b] be an unobserved functional random variable. For a fixed t, we can observe a random variable Y(t) which, conditional on X(t), follows a parametric model having X(t) as one of its parameters. A non-parametric smoothing procedure can be used to estimate X(t) from the observed data. Particular cases of this setting handle functional data with observation errors, or asume that functional data follow an exponential family model with one parameter depending on t.
In this work we present a general non-parametric smoothing procedure based on local likelihood approach which is valid for situations not entering in the exponential family and/or having more than one parameter depending on t.
We apply our proposals to model continuous monitoring glucose curves. First, glucose values are rescaled to the interval [0,1], considering the historical minimum and maximum observed values for each individual. Then a Beta distribution with parameters smoothly depending on t is assumed.