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Achraf Cohen authored and Achraf Cohen committed Jun 26, 2023
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<meta name="dcterms.date" content="2022-10-25">
<meta name="dcterms.date" content="2023-06-26">

<title>Report Sample</title>
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<div>
<div class="quarto-title-meta-heading">Published</div>
<div class="quarto-title-meta-contents">
<p class="date">October 25, 2022</p>
<p class="date">June 26, 2023</p>
</div>
</div>


</div>

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<section id="introduction" class="level2">
<h2 class="anchored" data-anchor-id="introduction">Introduction</h2>
<p>Kernel regression is a non-parametric estimator that estimates the conditional expectation of two variables which is random. The goal of a kernel regression is to discover the non-linear relationship between two random variables. To discover the non-linear relationship, kernel estimator or kernel smoothing is the main method to estimate the curve for non-parametric statistics. In kernel estimator, weight function is known as kernel function <span class="citation" data-cites="efr2008">(<a href="#ref-efr2008" role="doc-biblioref">Efromovich 2008</a>)</span>. Cite this paper <span class="citation" data-cites="bro2014principal">(<a href="#ref-bro2014principal" role="doc-biblioref">Bro and Smilde 2014</a>)</span>.</p>
<p>Kernel regression is a non-parametric estimator that estimates the conditional expectation of two variables which is random. The goal of a kernel regression is to discover the non-linear relationship between two random variables. To discover the non-linear relationship, kernel estimator or kernel smoothing is the main method to estimate the curve for non-parametric statistics. In kernel estimator, weight function is known as kernel function <span class="citation" data-cites="efr2008">(<a href="#ref-efr2008" role="doc-biblioref">Efromovich 2008</a>)</span>. Cite this paper <span class="citation" data-cites="bro2014principal">(<a href="#ref-bro2014principal" role="doc-biblioref">Bro and Smilde 2014</a>)</span>. The GEE <span class="citation" data-cites="wang2014">(<a href="#ref-wang2014" role="doc-biblioref">Wang 2014</a>)</span>.</p>
</section>
<section id="methods" class="level2">
<h2 class="anchored" data-anchor-id="methods">Methods</h2>
<p>The common non-parametric regression model is <span class="math inline">\(Y_i = m(X_i) + \varepsilon_i\)</span>, where <span class="math inline">\(Y_i\)</span> can be defined as the sum of the regression function value <span class="math inline">\(m(x)\)</span> for <span class="math inline">\(X_i\)</span>. Here <span class="math inline">\(m(x)\)</span> is unknown and <span class="math inline">\(\varepsilon_i\)</span> some errors. With the help of this definition, we can create the estimation for local averaging i.e.&nbsp;<span class="math inline">\(m(x)\)</span> can be estimated with the product of <span class="math inline">\(Y_i\)</span> average and <span class="math inline">\(X_i\)</span> is near to <span class="math inline">\(x\)</span>. In other words, this means that we are discovering the line through the data points with the help of surrounding data points. The estimation formula is printed below <span class="citation" data-cites="R-base">(<a href="#ref-R-base" role="doc-biblioref">R Core Team 2019</a>)</span>:</p>
<p><span class="math display">\[
M_n(x) = \sum_{i=1}^{n} W_n (X_i) Y_i \tag{1}
\]</span></p>
<p><span class="math inline">\(W_n(x)\)</span> is the sum of weights that belongs to all real numbers. Weights are positive numbers and small if <span class="math inline">\(X_i\)</span> is far from <span class="math inline">\(x\)</span>.</p>
\]</span> <span class="math inline">\(W_n(x)\)</span> is the sum of weights that belongs to all real numbers. Weights are positive numbers and small if <span class="math inline">\(X_i\)</span> is far from <span class="math inline">\(x\)</span>.</p>
</section>
<section id="analysis-and-results" class="level2">
<h2 class="anchored" data-anchor-id="analysis-and-results">Analysis and Results</h2>
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<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a><span class="fu">kable</span>(<span class="fu">head</span>(murders))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<th style="text-align: left;">state</th>
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</section>

<div id="quarto-appendix" class="default"><section class="quarto-appendix-contents" role="doc-bibliography"><h2 class="anchored quarto-appendix-heading">References</h2><div id="refs" class="references csl-bib-body hanging-indent" role="doc-bibliography">
<div id="ref-bro2014principal" class="csl-entry" role="doc-biblioentry">
<div id="quarto-appendix" class="default"><section class="quarto-appendix-contents" role="doc-bibliography"><h2 class="anchored quarto-appendix-heading">References</h2><div id="refs" class="references csl-bib-body hanging-indent" role="list">
<div id="ref-bro2014principal" class="csl-entry" role="listitem">
Bro, Rasmus, and Age K Smilde. 2014. <span>“Principal Component Analysis.”</span> <em>Analytical Methods</em> 6 (9): 2812–31.
</div>
<div id="ref-efr2008" class="csl-entry" role="doc-biblioentry">
<div id="ref-efr2008" class="csl-entry" role="listitem">
Efromovich, S. 2008. <em>Nonparametric Curve Estimation: Methods, Theory, and Applications</em>. Springer Series in Statistics. Springer New York. <a href="https://books.google.com/books?id=mdoLBwAAQBAJ">https://books.google.com/books?id=mdoLBwAAQBAJ</a>.
</div>
<div id="ref-R-base" class="csl-entry" role="doc-biblioentry">
<div id="ref-R-base" class="csl-entry" role="listitem">
R Core Team. 2019. <em>R: A Language and Environment for Statistical Computing</em>. Vienna, Austria: R Foundation for Statistical Computing. <a href="https://www.R-project.org">https://www.R-project.org</a>.
</div>
<div id="ref-wang2014" class="csl-entry" role="listitem">
Wang, Ming. 2014. <span>“Generalized Estimating Equations in Longitudinal Data Analysis: A Review and Recent Developments.”</span> <em>Advances in Statistics</em> 2014.
</div>
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