A0170
Title: Generalized functional linear models under choice-based sampling
Authors: Sophie Dabo - University of Lille (France) [presenting]
Mohamed Salem Ahmed - University of Lille (France)
Abstract: A functional binary model in a context of sampling data is proposed and estimated. This problem is known respectively in econometric and epidemiology literatures, as Choice-Based Sampling and case-control study, in discrete choice model. Unlike the random sample where all items in the population have the same probability of being chosen, the Choice-Based Sampling (CBS) in discrete choice model is a type of sampling where the classification of the population into subsets to be sampled is based on the choices or outcomes. In practice, it could be of interest to model choice of individuals using some functional covariates instead of real valued random variables. To this end, we introduce the Choice-Based sampling in a functional framework (functional generalized linear models). We reduce the infinite dimensional of the space of the explanatory random function using a Karhunen-Loeve expansion and maximize a conditional likelihood function. Our method is based on the components of a Functional Principal Components Analysis adapted to the context of Choice-Based Sampling. Asymptotic properties of our estimate are given. We present some simulated experiments including genetic data, to investigate the finite sample performance of the estimation method. The potential of the functional choice-based sampling model to integrate the special non-random features of the sample, that would have been hard to see otherwise is also outlined.
