{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T13:40:25Z","timestamp":1772372425458,"version":"3.50.1"},"reference-count":14,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2017,12,31]],"date-time":"2017-12-31T00:00:00Z","timestamp":1514678400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, a robust version of the Wald test statistic for composite likelihood is considered by using the composite minimum density power divergence estimator instead of the composite maximum likelihood estimator. This new family of test statistics will be called Wald-type test statistics. The problem of testing a simple and a composite null hypothesis is considered, and the robustness is studied on the basis of a simulation study. The composite minimum density power divergence estimator is also introduced, and its asymptotic properties are studied.<\/jats:p>","DOI":"10.3390\/e20010018","type":"journal-article","created":{"date-parts":[[2018,1,3]],"date-time":"2018-01-03T12:00:06Z","timestamp":1514980806000},"page":"18","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Composite Likelihood Methods Based on Minimum Density Power Divergence Estimator"],"prefix":"10.3390","volume":"20","author":[{"given":"Elena","family":"Castilla","sequence":"first","affiliation":[{"name":"Department of Statistics and O.R. I, Complutense University of Madrid, 28040 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4766-1909","authenticated-orcid":false,"given":"Nirian","family":"Mart\u00edn","sequence":"additional","affiliation":[{"name":"Department of Statistics and O.R. II, Complutense University of Madrid, 28003 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Leandro","family":"Pardo","sequence":"additional","affiliation":[{"name":"Department of Statistics and O.R. I, Complutense University of Madrid, 28040 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Konstantinos","family":"Zografos","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,12,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1093\/biomet\/85.3.549","article-title":"Robust and efficient estimation by minimizing a density power divergence","volume":"85","author":"Basu","year":"1998","journal-title":"Biometrika"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1007\/s10463-012-0372-y","article-title":"Testing statistical hypotheses based on the density power divergence","volume":"65","author":"Basu","year":"2013","journal-title":"Ann. Inst. Stat. Math."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1007\/s00184-014-0518-4","article-title":"Robust tests for the equality of two normal means based on the density power divergence","volume":"78","author":"Basu","year":"2015","journal-title":"Metrika"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/02331888.2015.1016435","article-title":"Generalized Wald-type tests based on minimum density power divergence estimators","volume":"50","author":"Basu","year":"2016","journal-title":"Statistics"},{"key":"ref_5","first-page":"2741","article-title":"A Wald-type test statistic for testing linear hypothesis in logistic regression models based on minimum density power divergence estimator","volume":"11","author":"Basu","year":"2017","journal-title":"Electon. J. Stat."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1016\/j.jmva.2016.01.004","article-title":"Influence analysis of robust Wald-type tests","volume":"147","author":"Ghosh","year":"2016","journal-title":"J. Multivar. Anal."},{"key":"ref_7","first-page":"4","article-title":"An overview of composite likelihood methods","volume":"21","author":"Varin","year":"2011","journal-title":"Stat. Sin."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3047","DOI":"10.1016\/j.jspi.2011.03.026","article-title":"On the robustness of maximum composite estimate","volume":"141","author":"Xu","year":"2011","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_9","unstructured":"Joe, H., Reid, N., Somg, P.X., Firth, D., and Varin, C. (2017, December 28). Composite Likelihood Methods. Available online: http:\/\/www.birs.ca\/events\/2012\/5-day-workshops\/12w5046."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1090\/conm\/080\/999014","article-title":"Composite likelihood methods","volume":"80","author":"Lindsay","year":"1998","journal-title":"Contemp. Math."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Basu, A., Shioya, H., and Park, C. (2011). Statistical Inference: The Minimum Distance Approach, Chapman & Hall\/CRC.","DOI":"10.1201\/b10956"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Maronna, R.A., Martin, R.D., and Yohai, V.J. (2006). Time Series, in Robust Statistics: Theory and Methods, John Wiley & Sons, Ltd.","DOI":"10.1002\/0470010940"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Mart\u00edn, N., Pardo, L., and Zografos, K. (2017). On divergence tests for composite hypotheses under composite likelihood. Statistical Papers, Springer.","DOI":"10.1007\/s00362-017-0900-1"},{"key":"ref_14","unstructured":"Pardo, L. (2006). Statistical Inference Based on Divergence Measures, Chapman & Hall\/CRC."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/1\/18\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:56:10Z","timestamp":1760208970000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/1\/18"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12,31]]},"references-count":14,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1]]}},"alternative-id":["e20010018"],"URL":"https:\/\/doi.org\/10.3390\/e20010018","relation":{"has-preprint":[{"id-type":"doi","id":"10.20944\/preprints201711.0039.v1","asserted-by":"object"}]},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,12,31]]}}}