{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T14:40:06Z","timestamp":1723128006494},"reference-count":0,"publisher":"Informa UK Limited","issue":"1","license":[{"start":{"date-parts":[[1999,1,1]],"date-time":"1999-01-01T00:00:00Z","timestamp":915148800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics and Decision Sciences"],"published-print":{"date-parts":[[1999,1,1]]},"abstract":"<jats:p>This paper is concerned with the application of an asymptotic quasi-likelihood\npractical procedure to estimate the unknown parameters in linear stochastic models of the form\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>y<\/mml:mi><mml:mi>t<\/mml:mi><\/mml:msub><mml:mo>=<\/mml:mo><mml:msub><mml:mi>f<\/mml:mi><mml:mi>t<\/mml:mi><\/mml:msub><mml:mrow><mml:mo>(<\/mml:mo><mml:mi>\u03b8<\/mml:mi><mml:mo>)<\/mml:mo><\/mml:mrow><mml:mo>+<\/mml:mo><mml:msub><mml:mi>M<\/mml:mi><mml:mi>t<\/mml:mi><\/mml:msub><mml:mrow><mml:mo>(<\/mml:mo><mml:mi>\u03b8<\/mml:mi><mml:mo>)<\/mml:mo><\/mml:mrow><\/mml:math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mo>(<\/mml:mo><mml:mrow><mml:mi>t<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>1<\/mml:mn><mml:mo>,<\/mml:mo><mml:mn>2<\/mml:mn><mml:mo>,<\/mml:mo><mml:mn>..<\/mml:mn><mml:mo>,<\/mml:mo><mml:mi>T<\/mml:mi><\/mml:mrow><mml:mo>)<\/mml:mo><\/mml:mrow><\/mml:math>\n, where <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:msub><mml:mi>f<\/mml:mi><mml:mi>t<\/mml:mi><\/mml:msub><\/mml:mrow><\/mml:math>\n is a linear predictable process of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03b8<\/mml:mi><\/mml:math>\n and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>M<\/mml:mi><mml:mi>t<\/mml:mi><\/mml:msub><\/mml:math>\n is an\nerror term such that <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>E<\/mml:mi><mml:mrow><mml:mo>(<\/mml:mo><mml:mrow><mml:msub><mml:mi>M<\/mml:mi><mml:mi>t<\/mml:mi><\/mml:msub><mml:mo>|<\/mml:mo><mml:msub><mml:mi>F<\/mml:mi><mml:mi>t<\/mml:mi><\/mml:msub><mml:mo>\u2212<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:mrow><mml:mo>)<\/mml:mo><\/mml:mrow><mml:mo>=<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:math>\n and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>E<\/mml:mi><mml:mrow><mml:mo>(<\/mml:mo><mml:mrow><mml:msubsup><mml:mi>M<\/mml:mi><mml:mi>t<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msubsup><mml:mo>|<\/mml:mo><mml:msub><mml:mi>F<\/mml:mi><mml:mi>t<\/mml:mi><\/mml:msub><mml:mo>\u2212<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:mrow><mml:mo>)<\/mml:mo><\/mml:mrow><mml:mo>&lt;<\/mml:mo><mml:mi>\u221e<\/mml:mi><\/mml:math>\n and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>F<\/mml:mi><\/mml:math>\nis a <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03c3<\/mml:mi><\/mml:math>-field generated\nfrom<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:msub><mml:mrow><mml:mrow><mml:mo>{<\/mml:mo><mml:mrow><mml:msub><mml:mi>y<\/mml:mi><mml:mi>s<\/mml:mi><\/mml:msub><\/mml:mrow><mml:mo>}<\/mml:mo><\/mml:mrow><\/mml:mrow><mml:mrow><mml:mi>s<\/mml:mi><mml:mo>\u2264<\/mml:mo><mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>\n. For this model, to estimate the parameter <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03b8<\/mml:mi><mml:mo>\u2208<\/mml:mo><mml:mi>\u0398<\/mml:mi><\/mml:math>, the ordinary least squares\nmethod is usually inappropriate (if there is only one observable path of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mo>{<\/mml:mo><mml:mrow><mml:msub><mml:mi>y<\/mml:mi><mml:mi>t<\/mml:mi><\/mml:msub><\/mml:mrow><mml:mo>}<\/mml:mo><\/mml:mrow><\/mml:math> and if <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>E<\/mml:mi><mml:mrow><mml:mo>(<\/mml:mo><mml:mrow><mml:mrow><mml:mrow><mml:msubsup><mml:mi>M<\/mml:mi><mml:mi>t<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msubsup><\/mml:mrow><mml:mo>|<\/mml:mo><mml:mrow\/><\/mml:mrow><mml:msub><mml:mi>F<\/mml:mi><mml:mi>t<\/mml:mi><\/mml:msub><mml:mo>\u2212<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:mrow><mml:mo>)<\/mml:mo><\/mml:mrow><\/mml:math>\nis not a constant) and the maximum likelihood method either does not exist or is mathematically\nintractable. If the finite dimensional distribution of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>M<\/mml:mi><mml:mi>t<\/mml:mi><\/mml:msub><\/mml:math>\n is unknown, to obtain a good estimate of\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03b8<\/mml:mi><\/mml:math>\n an appropriate predictable process <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>g<\/mml:mi><mml:mi>t<\/mml:mi><\/mml:msub><\/mml:math> should be determined. In this paper, criteria for determining\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>g<\/mml:mi><mml:mi>t<\/mml:mi><\/mml:msub><\/mml:math>\n are introduced which, if satisfied, provide more accurate estimates of the parameters via the\nasymptotic quasi-likelihood method.<\/jats:p>","DOI":"10.1155\/s1173912699000024","type":"journal-article","created":{"date-parts":[[2007,3,8]],"date-time":"2007-03-08T07:44:28Z","timestamp":1173339868000},"page":"21-39","source":"Crossref","is-referenced-by-count":2,"title":["A practical procedure for estimation of linear models via\nasymptotic quasi-likelihood"],"prefix":"10.1080","volume":"3","author":[{"given":"Riccardo","family":"Biondini","sequence":"first","affiliation":[{"name":"School of Mathematics and Applied Statistics, University of Wollongong, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yan-Xia","family":"Lin","sequence":"additional","affiliation":[{"name":"School of Mathematics and Applied Statistics, University of Wollongong, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sifa","family":"Mvoi","sequence":"additional","affiliation":[{"name":"School of Mathematics and Applied Statistics, University of Wollongong, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"301","container-title":["Journal of Applied Mathematics and Decision Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/archive\/1999\/746525.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/archive\/1999\/746525.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T14:22:57Z","timestamp":1723126977000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/ads\/1999\/746525\/abs\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,1,1]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1999,1,1]]}},"alternative-id":["746525"],"URL":"https:\/\/doi.org\/10.1155\/s1173912699000024","relation":{},"ISSN":["1173-9126"],"issn-type":[{"type":"print","value":"1173-9126"}],"subject":[],"published":{"date-parts":[[1999,1,1]]}}}