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Zhang, Tong; Sun, Zhihua; Sun, Liuquan

Goodness-of-fit test for partial functional linear model with errors in scalar covariates. (English) Zbl 07714068

J. Stat. Plann. Inference 227, 91-111 (2023).
Summary: In this article, we study the adequacy test of the partial functional linear model when the scalar predictors are measured with additive errors. Based on a corrected profile least-squares estimation of the null model, estimated residuals are first constructed, and a U-statistic-based test is proposed. The asymptotic properties of the test are investigated under the null and the alternative hypotheses. It is shown that the proposed test can control the type I error well, and its power performance is satisfactory. The finite sample performance of the proposed test is demonstrated through simulation studies and a real data analysis.

MSC:

62-XX Statistics

Keywords:

additive measurement errors; functional covariate; goodness-of-fit test; partial functional linear model; U-statistic-based test

Software:

rp.flm.test; fda (R)
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Full Text: DOI

References:

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