Measures of Influence in the Functional Linear Model with Scalar Response Articles uri icon

publication date

  • January 2010

start page

  • 305

end page

  • 490

issue

  • 2

volume

  • 101

international standard serial number (ISSN)

  • 0047-259X

electronic international standard serial number (EISSN)

  • 1095-7243

abstract

  • This paper studies how to identify influential observations in the functional linear model in which the predictor is functional and the response is scalar. Measurement of the effects of a single observation
    on estimation and prediction when the model is estimated by the
    principal components method is undertaken. For that, three statistics
    are introduced for measuring the influence of each observation on
    estimation and prediction of the functional linear model with scalar
    response that are generalizations of the measures proposed for the
    standard regression model by [D.R. Cook, Detection of influential
    observations in linear regression, Technometrics 19 (1977) 15&-18; D.
    Peña, A new statistic for influence in linear regression, Technometrics
    47 (2005) 1&-12] respectively. A smoothed bootstrap method is proposed to
    estimate the quantiles of the influence measures, which allows us to
    point out which observations have the larger influence on estimation and
    prediction. The behavior of the three statistics and the quantile
    estimation bootstrap based method is analyzed via a simulation study.
    Finally, the practical use of the proposed statistics is illustrated by
    the analysis of a real data example, which show that the proposed
    measures are useful for detecting heterogeneity in the functional linear
    model with scalar response.