Document Zbl 07632855

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Stat.</a> <a href="/?q=in%3A491037" title="Articles in this Issue">75, No. 2, 195-206 (2021)</a>. </div> <div class="abstract"></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7632855">Cited in <strong>11</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62-XX" title="MSC2020">62-XX</a> </td> <td class="space"> Statistics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aexperimental+design">experimental design</a>; <a href="/?q=ut%3Aoptimization">optimization</a>; <a href="/?q=ut%3Arandomization">randomization</a>; <a href="/?q=ut%3Arestricted+randomization">restricted randomization</a></div> <div class="software"> <h3>Software:</h3><a href="/software/18151">GreedyExperimentalDesign</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 07632855" data-ciurl="/ci/07632855" data-biburl="/bibtex/07632855.bib" data-amsurl="/amsrefs/07632855.bib" data-xmlurl="/xml/07632855.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07632855.pdf" title="Zbl 07632855 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/10.1080/00031305.2020.1717619" aria-label="DOI for “Harmonizing optimized designs with classic randomization in experiments”" title="10.1080/00031305.2020.1717619">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://figshare.com/articles/journal_contribution/Harmonizing_Optimized_Designs_with_Classic_Randomization_in_Experiments/11673603" title="Full Text Link">Link</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Berk, R.; Barnes, G.; Ahlman, L.; Kurtz, E., “When Second Best Is Good Enough: A Comparison Between a True Experiment and a Regression Discontinuity Quasi-Experiment, Journal of Experimental Criminology, 6, 191-208 (2010) · <a href="https://doi.org/10.1007/s11292-010-9095-3" class="nowrap">doi:10.1007/s11292-010-9095-3</a></td> </tr><tr> <td>[2]</td> <td class="space">Bertsimas, D.; Johnson, M.; Kallus, N., “The Power of Optimization Over Randomization in Designing Experiments Involving Small Samples, Operations Research, 63, 868-876 (2015) · <a href="/1329.90078" class="nowrap">Zbl 1329.90078</a> · <a href="https://doi.org/10.1287/opre.2015.1361" class="nowrap">doi:10.1287/opre.2015.1361</a></td> </tr><tr> <td>[3]</td> <td class="space">Cornfield, J., “Principles of Research, American Journal of Mental Deficiency, 64, 240-252 (1959)</td> </tr><tr> <td>[4]</td> <td class="space">Efron, B., “Forcing a Sequential Experiment to Be Balanced, Biometrika, 58, 403-417 (1971) · <a href="/0226.62086" class="nowrap">Zbl 0226.62086</a> · <a href="https://doi.org/10.1093/biomet/58.3.403" class="nowrap">doi:10.1093/biomet/58.3.403</a></td> </tr><tr> <td>[5]</td> <td class="space">Fisher, R. A., Statistical Methods for Research Workers (1925), Edinburgh: Oliver & Boyd, Edinburgh · <a href="/51.0414.08" class="nowrap">JFM 51.0414.08</a></td> </tr><tr> <td>[6]</td> <td class="space">Fisher, R. A., The Design of Experiments (1935), Edinburgh: Oliver and Boyd, Edinburgh</td> </tr><tr> <td>[7]</td> <td class="space">Freedman, D. A., “On Regression Adjustments to Experimental Data, Advances in Applied Mathematics, 40, 180-193 (2008) · <a href="/1130.62003" class="nowrap">Zbl 1130.62003</a> · <a href="https://doi.org/10.1016/j.aam.2006.12.003" class="nowrap">doi:10.1016/j.aam.2006.12.003</a></td> </tr><tr> <td>[8]</td> <td class="space">Garthwaite, P. H., “Confidence Intervals From Randomization Tests, Biometrics, 52, 1387-1393 (1996) · <a href="/0925.62122" class="nowrap">Zbl 0925.62122</a> · <a href="https://doi.org/10.2307/2532852" class="nowrap">doi:10.2307/2532852</a></td> </tr><tr> <td>[9]</td> <td class="space">Götze, F.; Tikhomirov, A., “Asymptotic Distribution of Quadratic Forms and Applications, Journal of Theoretical Probability, 15, 423-475 (2002) · <a href="/1002.60018" class="nowrap">Zbl 1002.60018</a> · <a href="https://doi.org/10.1023/A:1014867011101" class="nowrap">doi:10.1023/A:1014867011101</a></td> </tr><tr> <td>[10]</td> <td class="space">Greevy, R.; Lu, B.; Silber, J. H.; Rosenbaum, P., “Optimal Multivariate Matching Before Randomization, Biostatistics, 5, 263-275 (2004) · <a href="/1096.62078" class="nowrap">Zbl 1096.62078</a> · <a href="https://doi.org/10.1093/biostatistics/5.2.263" class="nowrap">doi:10.1093/biostatistics/5.2.263</a></td> </tr><tr> <td>[11]</td> <td class="space">Harville, D. A., “Experimental Randomization: Who Needs It?, The American Statistician, 29, 27-31 (1975) · <a href="/0361.62071" class="nowrap">Zbl 0361.62071</a> · <a href="https://doi.org/10.2307/2683676" class="nowrap">doi:10.2307/2683676</a></td> </tr><tr> <td>[12]</td> <td class="space">Imbens, G. W.; Rubin, D. B., Social, and Biomedical Sciences, Causal Inference in Statistics (2015), New York: Cambridge University Press, New York · <a href="/1355.62002" class="nowrap">Zbl 1355.62002</a></td> </tr><tr> <td>[13]</td> <td class="space">Kallus, N., “Optimal a Priori Balance in the Design of Controlled Experiments, Journal of the Royal Statistical Society, Series B, 80, 85-112 (2018) · <a href="/06840458" class="nowrap">Zbl 06840458</a> · <a href="https://doi.org/10.1111/rssb.12240" class="nowrap">doi:10.1111/rssb.12240</a></td> </tr><tr> <td>[14]</td> <td class="space">Kapelner, A., Krieger, A. M., Sklar, M., and Azriel, D. (2019), “Optimal Rerandomization via a Criterion That Provides Insurance Against Failed Experiments,” arXiv no. arXiv:1810.08389. · <a href="/1484.62126" class="nowrap">Zbl 1484.62126</a></td> </tr><tr> <td>[15]</td> <td class="space">Kempthorne, O., “The Randomization Theory of Experimental Inference, Journal of the American Statistical Association, 50, 946-967 (1955) · <a href="https://doi.org/10.2307/2281178" class="nowrap">doi:10.2307/2281178</a></td> </tr><tr> <td>[16]</td> <td class="space">Kiefer, J.; Wolfowitz, J., “Optimum Designs in Regression Problems, The Annals of Mathematical Statistics, 30, 271-294 (1959) · <a href="/0090.11404" class="nowrap">Zbl 0090.11404</a> · <a href="https://doi.org/10.1214/aoms/1177706252" class="nowrap">doi:10.1214/aoms/1177706252</a></td> </tr><tr> <td>[17]</td> <td class="space">Krieger, A. M.; Azriel, D.; Kapelner, A., “Nearly Random Designs With Greatly Improved Balance, Biometrika, 106, 695-701 (2019) · <a href="/1464.62357" class="nowrap">Zbl 1464.62357</a> · <a href="https://doi.org/10.1093/biomet/asz026" class="nowrap">doi:10.1093/biomet/asz026</a></td> </tr><tr> <td>[18]</td> <td class="space">Lachin, J. M., “Properties of Simple Randomization in Clinical Trials, Controlled Clinical Trials, 9, 312-326 (1988) · <a href="https://doi.org/10.1016/0197-2456(88)90046-3" class="nowrap">doi:10.1016/0197-2456(88)90046-3</a></td> </tr><tr> <td>[19]</td> <td class="space">Land, A. H.; Doig, A. G., “An Automatic Method of Solving Discrete Programming Problems, Econometrica, 28, 497-520 (1960) · <a href="/0101.37004" class="nowrap">Zbl 0101.37004</a> · <a href="https://doi.org/10.2307/1910129" class="nowrap">doi:10.2307/1910129</a></td> </tr><tr> <td>[20]</td> <td class="space">Li, X.; Ding, P.; Rubin, D. B., “Asymptotic Theory of Rerandomization in Treatment-Control Experiments, Proceedings of the National Academy of Sciences of the United States of America, 115, 9157-9162 (2018) · <a href="/1416.62440" class="nowrap">Zbl 1416.62440</a> · <a href="https://doi.org/10.1073/pnas.1808191115" class="nowrap">doi:10.1073/pnas.1808191115</a></td> </tr><tr> <td>[21]</td> <td class="space">Lin, W., “Agnostic Notes on Regression Adjustments to Experimental Data: Reexamining Freedman’s Critique, The Annals of Applied Statistics, 7, 295-318 (2013) · <a href="/1454.62217" class="nowrap">Zbl 1454.62217</a> · <a href="https://doi.org/10.1214/12-AOAS583" class="nowrap">doi:10.1214/12-AOAS583</a></td> </tr><tr> <td>[22]</td> <td class="space">Morgan, K. L.; Rubin, D. B., “Rerandomization to Improve Covariate Balance in Experiments, The Annals of Statistics, 40, 1263-1282 (2012) · <a href="/1274.62509" class="nowrap">Zbl 1274.62509</a> · <a href="https://doi.org/10.1214/12-AOS1008" class="nowrap">doi:10.1214/12-AOS1008</a></td> </tr><tr> <td>[23]</td> <td class="space">Rosenberger, W. F.; Lachin, J. M., Randomization in Clinical Trials: Theory and Practice (2016), Hoboken, NJ: Wiley, Hoboken, NJ · <a href="/1329.92004" class="nowrap">Zbl 1329.92004</a></td> </tr><tr> <td>[24]</td> <td class="space">Senn, S., “Seven Myths of Randomisation in Clinical Trials, Statistics in Medicine, 32, 1439-1450 (2013) · <a href="https://doi.org/10.1002/sim.5713" class="nowrap">doi:10.1002/sim.5713</a></td> </tr><tr> <td>[25]</td> <td class="space">Smith, K., “On the Standard Deviations of Adjusted and Interpolated Values of an Observed Polynomial Function and Its Constants and the Guidance They Give Towards a Proper Choice of the Distribution of Observations, Biometrika, 12, 1-85 (1918) · <a href="https://doi.org/10.1093/biomet/12.1-2.1" class="nowrap">doi:10.1093/biomet/12.1-2.1</a></td> </tr><tr> <td>[26]</td> <td class="space">Steinberg, D. M.; Hunter, W. G., “Experimental Design: Review and Comment, Technometrics, 26, 71-97 (1984) · <a href="/0549.62048" class="nowrap">Zbl 0549.62048</a> · <a href="https://doi.org/10.1080/00401706.1984.10487928" class="nowrap">doi:10.1080/00401706.1984.10487928</a></td> </tr><tr> <td>[27]</td> <td class="space">Student, “Comparison Between Balanced and Random Arrangements of Field Plots, Biometrika, 29, 363-378 (1938) · <a href="/64.1221.01" class="nowrap">JFM 64.1221.01</a> · <a href="https://doi.org/10.2307/2332011" class="nowrap">doi:10.2307/2332011</a></td> </tr><tr> <td>[28]</td> <td class="space">Verrill, S., “When Good Confidence Intervals Go Bad: Predictor Sort Experiments and ANOVA, The American Statistician, 53, 38-42 (1999) · <a href="https://doi.org/10.2307/2685650" class="nowrap">doi:10.2307/2685650</a></td> </tr><tr> <td>[29]</td> <td class="space">Wu, C.-F., “On the Robustness and Efficiency of Some Randomized Designs, The Annals of Statistics, 9, 1168-1177 (1981) · <a href="/0474.62075" class="nowrap">Zbl 0474.62075</a> · <a href="https://doi.org/10.1214/aos/1176345634" class="nowrap">doi:10.1214/aos/1176345634</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. 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