Document Zbl 1169.62027

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Stat.</a> <a href="/?q=in%3A245200" title="Articles in this Issue">37, No. 1, 35-72 (2009)</a>. </div> <div class="abstract">Summary: The paper considers functional linear regression, where scalar responses $Y_{1}, \dots , Y_n$ are modeled in dependence of random functions $X_{1}, \dots , X_n$. We propose a smoothing splines estimator for the functional slope parameter based on a slight modification of the usual penalty. Theoretical analysis concentrates on the error in an out-of-sample prediction of the response for a new random function $X_{n+1}$. It is shown that rates of convergence of the prediction error depend on the smoothness of the slope function and on the structure of the predictors. We then prove that these rates are optimal in the sense that they are minimax over large classes of possible slope functions and distributions of the predictive curves. For the case of models with errors-in-variables the smoothing spline estimator is modified by using a denoising correction of the covariance matrix of discretized curves. The methodology is then applied to a real case study where the aim is to predict the maximum of the concentration of ozone by using the curve of this concentration measured the preceding day.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5518687">Cited in <strong>157</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62G08" title="MSC2020">62G08</a> </td> <td class="space"> Nonparametric regression and quantile regression </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62J05" title="MSC2020">62J05</a> </td> <td class="space"> Linear regression; mixed models </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62G20" title="MSC2020">62G20</a> </td> <td class="space"> Asymptotic properties of nonparametric inference </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62G05" title="MSC2020">62G05</a> </td> <td class="space"> Nonparametric estimation </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62M20" title="MSC2020">62M20</a> </td> <td class="space"> Inference from stochastic processes and prediction </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Afunctional+linear+regression">functional linear regression</a>; <a href="/?q=ut%3Afunctional+parameter">functional parameter</a>; <a href="/?q=ut%3Afunctional+variable">functional variable</a>; <a href="/?q=ut%3Asmoothing+splines">smoothing splines</a></div> <div class="software"> <h3>Software:</h3><a href="/software/4511">fda (R)</a>; <a href="/software/5243">VanHuffel</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1169.62027" data-ciurl="/ci/05518687" data-biburl="/bibtex/05518687.bib" data-amsurl="/amsrefs/05518687.bib" data-xmlurl="/xml/05518687.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05518687.pdf" title="Zbl 1169.62027 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1214/07-AOS563" aria-label="DOI for “Smoothing splines estimators for functional linear regression”" title="10.1214/07-AOS563">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/0902.4344"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Aneiros-Perez, G., Cardot, H., Estevez-Perez, G. and Vieu, P. 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