RT Journal Article
T1 A goodness-of-fit test for the functional linear model with functional response
A1 García Portugués, Eduardo
A1 Álvarez Liébana, Javier
A1 Álvarez Pérez, Gonzalo
A1 González Manteiga, Wenceslao
AB The functional linear model with functional response (FLMFR) is one of the most fundamental models to assess the relation between two functional random variables. In this article, we propose a novel goodness-of-fit test for the FLMFR against a general, unspecified, alternative. The test statistic is formulated in terms of a Cramér–von Mises norm over a doubly projected empirical process which, using geometrical arguments, yields an easy-to-compute weighted quadratic norm. A resampling procedure calibrates the test through a wild bootstrap on the residuals and the use of convenient computational procedures. As a sideways contribution, and since the statistic requires a reliable estimator of the FLMFR, we discuss and compare several regularized estimators, providing a new one specifically convenient for our test. The finite sample behavior of the test is illustrated via a simulation study. Also, the new proposal is compared with previous significance tests. Two novel real data sets illustrate the application of the new test.
PB Wiley
SN 1467-9469
YR 2021
FD 2021
LK https://hdl.handle.net/20.500.14352/95397
UL https://hdl.handle.net/20.500.14352/95397
LA eng
NO García-Portugués, E. et al. (2021) «A goodness-of-fit test for the functional linear model with functional response», Scandinavian Journal of Statistics, 48(2), pp. 502-528. doi:10.1111/SJOS.12486.
NO Ministerio de Economía y Competitividad (España)
DS Docta Complutense
RD 17 abr 2025