Generalized Functional Linear Models under Choice-Based Sampling

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Dabo-Niang, Sophie | Ahmed, Mohamed Salem

Edité par HAL CCSD

We propose here to describe and estimate a functional binary model in a context of sampling data. 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, this paper introduces the Choice-Based sampling in a functional framework (functional generalized linear models). We adapt the approach of [31] to reduce the infinite dimensional of the space of the explanatory random function using a Karhunen –Lò eve 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. Then this expansion is truncated to a finite number of terms that asymp-totically increases with the sample size. Asymptotic properties of our estimate are ensured by the help of works of [4], [31]. We present some simulated experiments including genetic data, to investigate the finite sample performance of the estimation method. The proposed functional model leads to encouraging results. 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.

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