{"product_id":"missing-the-random-effect-when-the-parameter-space-is-expanding-von-ru-chen","title":"Missing the Random Effect","description":"\u003cp\u003eRevision with unchanged content. In this project we look at the case when two of fundamental assumptions in  the method of Maximum Likelihood are violated. In particular, we study a  special class of misspecified models, where the true model is a mixed effect  model but the working model is a fixed effect model with parameters of  dimension increasing with sample size. We provide a sufficient condition  under which the MLE derived from the working model converges to a welldefined  and asymptotically normally-distributed limit. In linear models, the  sample variance is biased; but there exists a robust variance estimator of the  MLE that converges to the true variance in probability. We also study the  Criterion-based automatic model selection methods and find that they may  select a linear model that contains spurious variables, but this can be avoided  by using the robust variance estimator for the MLE in Bonferroni-adjusted  model section or by choosing ¿n that grows fast enough in Shao's GIC. In  generalized linear models, general results are given and computational and  simulation studies are carried out to corroborate asymptotic theoretical  results as well as to calculate quantities that are not available in theoretical  calculation.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783639455144\"\u003e\u003ch3\u003eWhen the Parameter Space Is Expanding\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783639455144","offer_id":39439174402141,"sku":"9783639455144","price":79.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/1c6fd6b1-e1d2-45c6-8af9-9704bf0051d2.jpg?v=1772864547","url":"https:\/\/shop.autorenwelt.de\/en\/products\/missing-the-random-effect-when-the-parameter-space-is-expanding-von-ru-chen","provider":"Autorenwelt Shop","version":"1.0","type":"link"}