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Theory"],"published-print":{"date-parts":[[1986,12]]},"abstract":"<jats:p>The primary concern is to establish a fairly general framework in which estimators<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0266466600011646_inline1\"\/>resulting from estimating equations g<jats:sub>n\u03b8<\/jats:sub>= 0 are<jats:italic>not<\/jats:italic>consistent. This leads on to consistency by an intuitive route. Asymptotic distributions of consistent estimators are also touched upon, and the results are applied to various examples.<\/jats:p>","DOI":"10.1017\/s0266466600011646","type":"journal-article","created":{"date-parts":[[2010,10,18]],"date-time":"2010-10-18T09:11:55Z","timestamp":1287393115000},"page":"305-330","source":"Crossref","is-referenced-by-count":88,"title":["On Consistency and Inconsistency of Estimating Equations"],"prefix":"10.1017","volume":"2","author":[{"given":"Martin","family":"Crowder","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2010,10,18]]},"reference":[{"key":"S0266466600011646_ref036","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176345071"},{"key":"S0266466600011646_ref018","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177693066"},{"key":"S0266466600011646_ref033","first-page":"439","article-title":"Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method","volume":"61","author":"R.W.M","year":"1974","journal-title":"Biometrika"},{"key":"S0266466600011646_ref021","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1214\/aoms\/1177697731","article-title":"Asymptotic properties of non-linear least squares estimators","volume":"40","author":"I","year":"1969","journal-title":"Annals of Mathematical Statistics"},{"key":"S0266466600011646_ref032","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177729952"},{"key":"S0266466600011646_ref006","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1111\/j.2517-6161.1976.tb01565.x","article-title":"Maximum likelihood estimation for dependent observations","volume":"38","author":"J","year":"1976","journal-title":"Journal of the Royal Statistical Society"},{"key":"S0266466600011646_ref031","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177730288"},{"key":"S0266466600011646_ref028","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1214\/aos\/1176344080","article-title":"On consistency in time series analysis","volume":"6","author":"M","year":"1978","journal-title":"Annals of Statistics"},{"key":"S0266466600011646_ref025","first-page":"277","article-title":"On some asymptotic properties of maximum likelihood estimates and related Bayes' estimates","volume":"I","author":"LeCam","year":"1953","journal-title":"University of California Publications in Statistics"},{"key":"S0266466600011646_ref023","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1214\/aos\/1176344207","article-title":"On conditional least-squares estimation for stochastic processes","volume":"6","author":"A.","year":"1978","journal-title":"Annals of Statistics"},{"key":"S0266466600011646_ref010","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1090\/S0002-9947-1934-1501765-1","article-title":"Probability and statistics","volume":"36","author":"L","year":"1934","journal-title":"Transactions of the American Mathematical Society"},{"key":"S0266466600011646_ref024","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/0047-259X(79)90093-9","article-title":"Strong consistency of least-squares estimates in multiple regression II","volume":"9","author":"L.","year":"1979","journal-title":"Journal of Multivariate Analysis"},{"key":"S0266466600011646_ref008","volume-title":"Technical Report","volume":"13","author":"J","year":"1981"},{"key":"S0266466600011646_ref001","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177706538"},{"key":"S0266466600011646_ref034","doi-asserted-by":"publisher","DOI":"10.2307\/1911465"},{"key":"S0266466600011646_ref009","volume-title":"Elements of Continuous Multivariate Analysis","author":"P","year":"1969"},{"key":"S0266466600011646_ref017","unstructured":"17. 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