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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<!--
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<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta name="keywords" content="nprlab, nonparametric regression, toolbox, matlab"/>
<meta name="description" content=""/>
<meta http-equiv="content-type" content="text/html; charset=utf-8"/>
<title>NPRLab</title>
<link href="style.css" rel="stylesheet" type="text/css" media="screen"/>
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<body>
<div id="wrapper">
<div id="menu-wrapper">
<div id="menu" class="container">
<ul>
<li class="current_page_item"><a href="#intro">Home</a></li>
<li><a href="#download">Download</a></li>
<li><a href="#about">About</a></li>
</ul>
</div>
</div>
<div id="logo" class="container">
<h1><a href="#">NPRLab</a></h1>
<p>NonParametric Regression Laboratory for MATLAB</p>
</div>
<div id="page" class="container">
<div class="post">
<h2 class="title" id="intro"><a href="#">Introduction</a></h2>
<div class="entry">
<p>NPRLab is a MATLAB toolbox for nonparametric regression. In particular, it implements a variety of "linear estimators". A linear estimator $r_n(x)$ can be written as $$r_n(x) = ∑↙{i=1}↖nl_i(x)Y_i,$$ for each $x$. Defining the vectors $r = (r_n(x_1),...,r_n(x_n))^T$ and $Y = (Y_1,...,Y_n)^T$, one can write these as a matrix-vector product: $$r = LY,$$ with $L$ the smoother matrix and $L_{ij} = l_j(x_i)$.</p>
<p>NPRLab is built around and requires the <a href="http://www.esat.kuleuven.be/sista/lssvmlab/">LS-SVMlab toolbox</a> to work. The following linear estimators are currently implemented:</p>
<ul>
<li>Nadaraya-Watson,</li>
<li>Local polynomial regression,</li>
<li>Priestley-Chao,</li>
<li>Least Squares Support Vector Machines (through the LS-SVMlab toolbox).</li>
</ul>
<p>
Moreover, other linear estimators can easily be added to the toolbox.
Data rescaling and bandwidth tuning is done automatically by the software. Bandwidth tuning is done using (i) leave-one-out cross-validation, (ii) generalized cross-validation or (iii) Akaike information criterium corrected (AICC). Finally, the toolbox also features confidence interval estimation by the volume-of-tube formula both in a one-dimensional and multi-dimensional setting (see <a href="http://projecteuclid.org/euclid.aos/1176325631">Sun, J., and Loader, C. R. (1994). Simultaneous confidence bands for linear regression and smoothing. The Annals of Statistics, 1328-1345.</a>). The computation of the multi-dimensional volume-of-tube formula uses multiple cores of the CPU if the Parallel Computing toolbox is installed. The toolbox includes a number of examples that demonstrate the usage.
</p>
</div>
</div>
<!-- end #content -->
<div id="three-column" class="container">
<div id="tbox1">
<div class="box-style">
<div class="content">
<div class="image"><img src="images/nwconf.png" width="324" height="200" alt=""/></div>
<h2>One-dimensional kernel regression</h2>
<p>Nadaraya-Watson estimate (red) along with a 95% simultaneous confidence interval and the true underlying function $\exp^{-32(X-0.5)^2}$ (green).</p>
</div>
</div>
</div>
<div id="tbox2">
<div class="box-style">
<div class="content">
<div class="image"><img src="images/mvnpdflssvm.png" width="324" height="200" alt=""/></div>
<h2>Multi-dimensional kernel regression</h2>
<p>LS-SVM estimate (red) along with a 95% simultaneous confidence band and the true underlying function (shaded area). The underlying function is a bivariate normal distribution.</p>
</div>
</div>
</div>
<div id="tbox3">
<div class="box-style">
<div class="content">
<div class="image"><img src="images/multidimcputime.png" width="324" height="200" alt=""/></div>
<h2>Accuracy vs. computation time</h2>
<p>The accuracy of the multi-dimensional volume-of-tube approximation is customizable: choose 3-term, 2-term or 1-term approximation for decreasing accuracy and increasing speed. The figure shows the computation time for a dataset of size N = 576.</p>
</div>
</div>
</div>
</div>
</div>
<div id="pagecont" class="container">
<div class="post">
<h2 class="title" id="download"><a href="#">Download and install</a></h2>
<div class="entry">
<p>NPRLab is released under the <a href="https://gnu.org/licenses/gpl.txt">GNU GPLv3 license</a>.</p>
<div class="button">
<a href="NPRLab.zip">Download</a>
</div>
<p>Installation steps:</p>
<ol>
<li>Download LS-SVMlab <a href="http://www.esat.kuleuven.be/sista/lssvmlab/">here</a>, unzip into a folder of choice and add the folder to the MATLAB path.</li>
<li>Download and unzip NPRLab into a folder of choice.</li>
<li>Run "install.m" within the NPRLab folder to add the required folders to the MATLAB path.</li>
<li>Run one of the examples in the "examples" folder. (optional)</li>
</ol>
<p>A short quickguide to the basic usage is available <a href="NPRLabquickguide.pdf">here</a>. The examples in the "examples" subfolder should also help to get you started. In addition, use the MATLAB 'help' function to get additional information on the functionality.</p>
<p>Known issues/bugs:</p>
<ul>
<li>If dim(X) > 1 and the degree of the local polynomial p > 1, then local polynomial regression gives incorrect results. All other cases work fine.</li>
</ul>
<p><a><img src="https://gnu.org/graphics/gplv3-88x31.png" alt=""/></a></p>
</div>
</div>
<div class="post">
<h2 class="title" id="about"><a href="#">About the author</a></h2>
<div class="entry">
<p>Pieter Jan Kerstens is a postdoctoral researcher in economics at the Department of Food and Resource Economics of the University of Copenhagen (Denmark). He obtained a PhD in economics from KU Leuven (Belgium), master degrees in economics and mathematical engineering at KU Leuven (Belgium) and a bachelor degree in computer science at Universiteit Antwerpen (Belgium). Feel free to contact him with any bugs/comments/suggestions you have at
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<p>
I'd love to hear how NPRLab is used, so if you use NPRLab then feel free to drop me a note saying where and how you used it. If you use this toolbox in any work then I kindly ask you to give credit by appropriately citing the quickguide or this website where possible.
</p>
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<a href="https://be.linkedin.com/in/pieter-jan-kerstens-6306aa57">
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<p>© 2014-2019 Pieter Jan Kerstens. All rights reserved. Design based on the domestic template by <a href="http://www.freecsstemplates.org">FCT</a>.</p>
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