Document Zbl 1499.62185

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J. Stat. Data Sci.</a> <a href="/?q=in%3A490982" title="Articles in this Issue">5, No. 2, 577-628 (2022)</a>. </div> <div class="abstract">Summary: Shrinkage estimation of Poisson means is considered when observations are given in the form of a two-way contingency table. Assuming a multiplicative Poisson model, estimators which shrink to the specified values or an order statistic in one dimension and in two dimensions are considered and are shown to dominate the maximum-likelihood estimator (MLE) under normalized squared error loss. Furthermore, assuming the full model, shrinkage to the multiplicative model is devised to improve upon the unbiased estimator. Shrinkage is made after determining the basic cells, so that the observed frequency is not smaller than the estimated frequency for each of the other cells.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7632469">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62H17" title="MSC2020">62H17</a> </td> <td class="space"> Contingency tables </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ashrinkage+estimator">shrinkage estimator</a>; <a href="/?q=ut%3AClevenson-Zidek+estimator">Clevenson-Zidek estimator</a>; <a href="/?q=ut%3Amultiplicative+Poisson+model">multiplicative Poisson model</a>; <a href="/?q=ut%3Aorder+statistics">order statistics</a>; <a href="/?q=ut%3Aestimated+frequency">estimated frequency</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 1499.62185" data-ciurl="/ci/07632469" data-biburl="/bibtex/07632469.bib" data-amsurl="/amsrefs/07632469.bib" data-xmlurl="/xml/07632469.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07632469.pdf" title="Zbl 1499.62185 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/10.1007/s42081-022-00169-9" aria-label="DOI for “Simultaneous estimation of Poisson means in two-way contingency tables under normalized squared error loss”" title="10.1007/s42081-022-00169-9">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Chang, Y-T; Shinozaki, N., Estimation of ordered means of two Poisson distributions, Communications in Statistics-Theory and Methods, 35, 1993-2003 (2006) · <a href="/1107.62021" class="nowrap">Zbl 1107.62021</a> · <a href="https://doi.org/10.1080/03610920600762848" class="nowrap">doi:10.1080/03610920600762848</a></td> </tr><tr> <td>[2]</td> <td class="space">Chang, Y-T; Shinozaki, N., New types of shrinkage estimators of Poisson means under the normalized squared error loss, Communications in Statistics-Theory and Methods, 48, 1108-1122 (2019) · <a href="/07530872" class="nowrap">Zbl 07530872</a> · <a href="https://doi.org/10.1080/03610926.2018.1423699" class="nowrap">doi:10.1080/03610926.2018.1423699</a></td> </tr><tr> <td>[3]</td> <td class="space">Chou, JP, Simultaneous estimation in discrete multivariate exponential families, The Annals of Statistics, 19, 314-328 (1991) · <a href="/0728.62033" class="nowrap">Zbl 0728.62033</a> · <a href="https://doi.org/10.1214/aos/1176347984" class="nowrap">doi:10.1214/aos/1176347984</a></td> </tr><tr> <td>[4]</td> <td class="space">Clevenson, M.; Zidek, J., Simultaneous estimation of the means of independent Poisson Laws, Journal of the American Statistical Association, 70, 698-705 (1975) · <a href="/0308.62018" class="nowrap">Zbl 0308.62018</a></td> </tr><tr> <td>[5]</td> <td class="space">Ghosh, M.; Hwang, JT; Tsui, KW, Construction of improved estimators in multiparameter estimation for discrete exponential families, The Annals of Statistics, 11, 351-367 (1983) · <a href="/0533.62027" class="nowrap">Zbl 0533.62027</a> · <a href="https://doi.org/10.1214/aos/1176346143" class="nowrap">doi:10.1214/aos/1176346143</a></td> </tr><tr> <td>[6]</td> <td class="space">Ghosh, M.; Yang, MC, Simultaneous estimation of Poisson means under entropy loss, The Annals of Statistics, 16, 278-291 (1988) · <a href="/0654.62012" class="nowrap">Zbl 0654.62012</a> · <a href="https://doi.org/10.1214/aos/1176350705" class="nowrap">doi:10.1214/aos/1176350705</a></td> </tr><tr> <td>[7]</td> <td class="space">Hamura, Y.; Kubokawa, T., Simultaneous estimation of parameters of Poisson distributions with unbalanced sample sizes, Japanese Journal of Statistics and Data Science, 2, 2, 405-435 (2019) · <a href="/1436.62079" class="nowrap">Zbl 1436.62079</a> · <a href="https://doi.org/10.1007/s42081-019-00039-x" class="nowrap">doi:10.1007/s42081-019-00039-x</a></td> </tr><tr> <td>[8]</td> <td class="space">Hara, H.; Takemura, A., Simultaneous estimation of the means in some Poisson log linear models, Journal of the Japan Statistical Society, 36, 17-36 (2006) · <a href="/1134.62320" class="nowrap">Zbl 1134.62320</a> · <a href="https://doi.org/10.14490/jjss.36.17" class="nowrap">doi:10.14490/jjss.36.17</a></td> </tr><tr> <td>[9]</td> <td class="space">Hwang, JT, Improving upon standard estimators in discrete exponential families with applications to Poisson and negative binomial cases, The Annals of Statistics, 10, 857-867 (1982) · <a href="/0493.62008" class="nowrap">Zbl 0493.62008</a></td> </tr><tr> <td>[10]</td> <td class="space">Komaki, F., Simultaneous prediction of independent Poisson observables, The Annals of Statistics, 32, 1744-1769 (2004) · <a href="/1092.62036" class="nowrap">Zbl 1092.62036</a> · <a href="https://doi.org/10.1214/009053604000000445" class="nowrap">doi:10.1214/009053604000000445</a></td> </tr><tr> <td>[11]</td> <td class="space">Komaki, F., Simultaneous prediction for independent Poisson process with different durations, Journal of Multivariate Analysis, 141, 35-48 (2015) · <a href="/1325.60073" class="nowrap">Zbl 1325.60073</a> · <a href="https://doi.org/10.1016/j.jmva.2015.06.008" class="nowrap">doi:10.1016/j.jmva.2015.06.008</a></td> </tr><tr> <td>[12]</td> <td class="space">Peng, J. C. M. (1975). Simultaneous estimation of the parameters of independent Poisson distributions. Technical Reports 78. Department of Statistics, Stanford University.</td> </tr><tr> <td>[13]</td> <td class="space">Tsui, KW, Robustness of Clevenson-Zidek-type estimators, Journal of the American Statistical Association, 79, 152-157 (1984) · <a href="/0553.62032" class="nowrap">Zbl 0553.62032</a> · <a href="https://doi.org/10.1080/01621459.1984.10477078" class="nowrap">doi:10.1080/01621459.1984.10477078</a></td> </tr><tr> <td>[14]</td> <td class="space">Tsui, KW, Further developments on the robustness of Clevenson-Zidek-type means estimators, Journal of the American Statistical Association, 81, 176-180 (1986) · <a href="/0588.62080" class="nowrap">Zbl 0588.62080</a></td> </tr><tr> <td>[15]</td> <td class="space">Tsui, KW; Press, SJ, Simultaneous estimation of several Poisson parameters under k-normalized squared error loss, The Annals of Statistics, 10, 93-100 (1982) · <a href="/0484.62014" class="nowrap">Zbl 0484.62014</a> · <a href="https://doi.org/10.1214/aos/1176345692" class="nowrap">doi:10.1214/aos/1176345692</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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