Testing model assumptions in functional regression models

Authors:
Axel Bücher;Holger Dette;Gabriele Wieczorek
Affiliations:
-;-;-
Venue:
Journal of Multivariate Analysis
Year:
2011

Citing 5
Cited 0

Nonlinear statistical models

Nonlinear statistical models
Testing linear regression models using non-parametric regression estimators when errors are non-independent

Computational Statistics & Data Analysis
Regression analysis for a functional response

Technometrics
Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics)

Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics)
Changes in atmospheric radiation from the statistical point of view

Computational Statistics & Data Analysis

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Abstract

In the functional regression model where the responses are curves, new tests for the functional form of the regression and the variance function are proposed, which are based on a stochastic process estimating L^2-distances. Our approach avoids the explicit estimation of the functional regression and it is shown that normalized versions of the proposed test statistics converge weakly. The finite sample properties of the tests are illustrated by means of a small simulation study. It is also demonstrated that for small samples, bootstrap versions of the tests improve the quality of the approximation of the nominal level.