Testing for linearity in scalar¿on¿function regression with responses missing at random Articles uri icon

publication date

  • January 2024

start page

  • 3405

end page

  • 3429

volume

  • 39

International Standard Serial Number (ISSN)

  • 0943-4062

Electronic International Standard Serial Number (EISSN)

  • 1613-9658

abstract

  • A goodness-of-ft test for the Functional Linear Model with Scalar Response
    (FLMSR) with responses Missing at Random (MAR) is proposed in this paper. The
    test statistic relies on a marked empirical process indexed by the projected functional covariate and its distribution under the null hypothesis is calibrated using a
    wild bootstrap procedure. The computation and performance of the test rely on having an accurate estimator of the functional slope of the FLMSR when the sample
    has MAR responses. Three estimation methods based on the Functional Principal
    Components (FPCs) of the covariate are considered. First, the simplifed method
    estimates the functional slope by simply discarding observations with missing
    responses. Second, the imputed method estimates the functional slope by imputing the missing responses using the simplifed estimator. Third, the inverse probability weighted method incorporates the missing response generation mechanism
    when imputing. Furthermore, both cross-validation and LASSO regression are
    used to select the FPCs used by each estimator. Several Monte Carlo experiments
    are conducted to analyze the behavior of the testing procedure in combination with
    the functional slope estimators. Results indicate that estimators performing missingresponse imputation achieve the highest power. The testing procedure is applied to
    check for linear dependence between the average number of sunny days per year and
    the mean curve of daily temperatures at weather stations in Spain

subjects

  • Statistics

keywords

  • functional linear model; functional principal components; goodnessof-ft tests; marked empirical processes; missing at random; wild bootstrap