M. Febrero-Bande, P. Galeano San Miguel, E. García Portugués, W. González-Manteiga
We construct goodness-of-fit tests for the Functional Linear Model with Scalar Response (FLMSR) when some of the responses are Missing At Random (MAR). For that, we extend two existing testing procedures for the case where all the responses have been observed to the MAR case. Each testing procedure gives rise to two statistics based on two marked empirical processes indexed by the randomly projected functional covariate that depend on a proper estimate of the functional slope of the FLMSR. The statistics are relatively easy to compute and their distributions under the null hypothesis are simple to calibrate based on wild bootstrap procedures. The behaviour of the resulting testing procedures are compared by means of an extensive simulation study. Additionally, they are applied to two real data sets for checking whether the linear hypothesis holds.
Palabras clave: Functional linear model, Functional principal components, Goodness-of-fit tests, Marked empirical processes, Missing at random, Random projections.
Programado
GT06 Análisis de Datos Funcionales III. Contribuciones recientes
8 de junio de 2022 17:20
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