A goodness‐of‐fit test for the functional linear model with functional response

@article{GarciaPortugues2019AGT,
  title={A goodness‐of‐fit test for the functional linear model with functional response},
  author={Eduardo Garc'ia-Portugu'es and Javier 'Alvarez-Li'ebana and Gonzalo {\'A}lvarez‐P{\'e}rez and Wenceslao Gonz'alez-Manteiga},
  journal={Scandinavian Journal of Statistics},
  year={2019},
  volume={48},
  pages={502 - 528}
}
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… 

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References

SHOWING 1-10 OF 63 REFERENCES

A Goodness-of-Fit Test for the Functional Linear Model with Scalar Response

This article proposes a goodness-of-fit test for the null hypothesis of a functional linear model with scalar response. The test is based on a generalization to the functional framework of a previous

Goodness-of-fit tests for the functional linear model based on randomly projected empirical processes

We consider marked empirical processes indexed by a randomly projected functional covariate to construct goodness-of-fit tests for the functional linear model with scalar response. The test

A CONSISTENT DIAGNOSTIC TEST FOR REGRESSION MODELS USING PROJECTIONS

This paper proposes a consistent test for the goodness-of-fit of parametric regression models that overcomes two important problems of the existing tests, namely, the poor empirical power and size

Restricted likelihood ratio tests for linearity in scalar-on-function regression

This work proposes a procedure for testing the linearity of a scalar-on-function regression relationship and shows how the functional linear model can be represented as a simple mixed model nested within the FGAM, a recently developed extension of thefunctional linear model.

Classical testing in functional linear models

ABSTRACT We extend four tests common in classical regression – Wald, score, likelihood ratio and F tests – to functional linear regression, for testing the null hypothesis, that there is no

Testing hypotheses in the functional linear model

The functional linear model with scalar response is a regression model where the predictor is a random function defined on some compact set of ℝ and the response is scalar. The response is modelled

Projection-based nonparametric goodness-of-fit testing with functional covariates

This test is based on the remark that checking the no-effect of the functional covariate is equivalent to checking the nullity of the conditional expectation of the error term given a sufficiently rich set of projections of the covariate, and uses a kernel-based approach.

An updated review of Goodness-of-Fit tests for regression models

This survey intends to collect the developments on Goodness-of-Fit for regression models during the last 20 years, from the very first origins with the proposals based on the idea of the tests for

Testing the Predictor Effect on a Functional Response

ABSTRACT This article examines the problem of nonparametric testing for the no-effect of a random covariate (or predictor) on a functional response. This means testing whether the conditional
...