Document Zbl 1327.62234

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However, there are two obstacles that restrict the use of the smoothing spline in practical statistical work. Firstly, it becomes computationally prohibitive for large data sets because the number of basis functions roughly equals the sample size. Secondly, its global smoothing parameter can only provide a constant amount of smoothing, which often results in poor performances when estimating inhomogeneous functions. In this work, we introduce a class of adaptive smoothing spline models that is derived by solving certain stochastic differential equations with finite element methods. The solution extends the smoothing parameter to a continuous data-driven function, which is able to capture the change of the smoothness of the underlying process. The new model is Markovian, which makes Bayesian computation fast. A simulation study and real data example are presented to demonstrate the effectiveness of our method.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6522874">Cited in <strong>17</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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%3A62F15" title="MSC2020">62F15</a> </td> <td class="space"> Bayesian inference </td> </tr><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%3A60H10" title="MSC2020">60H10</a> </td> <td class="space"> Stochastic ordinary differential equations (aspects of stochastic analysis) </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aadaptive+smoothing">adaptive smoothing</a>; <a href="/?q=ut%3AMarkov+chain+Monte+Carlo">Markov chain Monte Carlo</a>; <a href="/?q=ut%3Asmoothing+spline">smoothing spline</a>; <a href="/?q=ut%3Astochastic+differential+equation">stochastic differential equation</a></div> <div class="software"> <h3>Software:</h3><a href="/software/11047">Fahrmeir</a>; <a href="/software/11132">gamair</a>; <a href="/software/7116">SemiPar</a>; <a href="/software/6641">GMRFLib</a>; <a href="/software/6099">gss</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 1327.62234" data-ciurl="/ci/06522874" data-biburl="/bibtex/06522874.bib" data-amsurl="/amsrefs/06522874.bib" data-xmlurl="/xml/06522874.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06522874.pdf" title="Zbl 1327.62234 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/10.1214/13-BA866" aria-label="DOI for “Bayesian adaptive smoothing splines using stochastic differential equations”" title="10.1214/13-BA866">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/1209.2013"title="Note: arXiv document may differ from published version">arXiv</a> <a class="btn btn-default btn-xs" type="button" href="https://projecteuclid.org/euclid.ba/1401148314" title="Full Text at Project Euclid">Euclid</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Abramovich, F. and Steinberg, D. 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