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In particular, the quadratic form estimator is consistent in a relative Frobenius norm sense provided <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S026646662000050X_inline1.png\"\/><jats:tex-math>\n${\\log }^3n\/T\\to 0$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. We obtain the limiting distributions of the Lagrange multiplier and Wald tests under both the null and local alternatives concerning the mean vector <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S026646662000050X_inline2.png\"\/><jats:tex-math>\n$\\mu $\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. Testing linear restrictions of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S026646662000050X_inline3.png\"\/><jats:tex-math>\n$\\mu $\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> is also investigated. Finally, our methodology is shown to perform well in finite sample situations both when the Kronecker product model is true and when it is not true.<\/jats:p>","DOI":"10.1017\/s026646662000050x","type":"journal-article","created":{"date-parts":[[2020,12,17]],"date-time":"2020-12-17T15:12:27Z","timestamp":1608217947000},"page":"1014-1067","source":"Crossref","is-referenced-by-count":3,"title":["ESTIMATION OF THE KRONECKER COVARIANCE MODEL BY QUADRATIC FORM"],"prefix":"10.1017","volume":"38","author":[{"given":"Oliver B.","family":"Linton","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haihan","family":"Tang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2020,12,17]]},"reference":[{"key":"S026646662000050X_r27","volume-title":"Theory and Application of Infinite 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