%0 Journal Article %1 kiefer_consistency_1956 %A Kiefer, J. %A Wolfowitz, J. %D 1956 %J The Annals of Mathematical Statistics %K effects nuissance, random %N 4 %P 887--906 %T Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters %U http://www.jstor.org/stable/2237188 %V 27 %X It is shown that, under usual regularity conditions, the maximum likelihood estimator of a structural parameter is strongly consistent, when the (infinitely many) incidental parameters are independently distributed chance variables with a common unknown distribution function. The latter is also consistently estimated although it is not assumed to belong to a parametric class. Application is made to several problems, in particular to the problem of estimating a straight line with both variables subject to error, which thus after all has a maximum likelihood solution.

@article{kiefer_consistency_1956, abstract = {It is shown that, under usual regularity conditions, the maximum likelihood estimator of a structural parameter is strongly consistent, when the (infinitely many) incidental parameters are independently distributed chance variables with a common unknown distribution function. The latter is also consistently estimated although it is not assumed to belong to a parametric class. Application is made to several problems, in particular to the problem of estimating a straight line with both variables subject to error, which thus after all has a maximum likelihood solution.}, added-at = {2017-01-09T13:57:26.000+0100}, author = {Kiefer, J. and Wolfowitz, J.}, biburl = {https://www.bibsonomy.org/bibtex/2ca25581e21088040625e6dc18a48d8bd/yourwelcome}, interhash = {3798ad631d407097663dac6bc228563d}, intrahash = {ca25581e21088040625e6dc18a48d8bd}, issn = {0003-4851}, journal = {The Annals of Mathematical Statistics}, keywords = {effects nuissance, random}, number = 4, pages = {887--906}, timestamp = {2017-01-09T14:01:11.000+0100}, title = {Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters}, url = {http://www.jstor.org/stable/2237188}, urldate = {2016-12-20}, volume = 27, year = 1956 }