Asymptotic properties of maximum quasi-likelihood estimator in quasi-likelihood nonlinear models with misspecified variance function

Statistics ◽  
2013 ◽  
Vol 48 (4) ◽  
pp. 778-786 ◽  
Author(s):  
Tian Xia ◽  
Xue-Ren Wang ◽  
Xue-Jun Jiang
Keyword(s):  
Nonlinear Models ◽  
Asymptotic Properties ◽  
Variance Function ◽  
Likelihood Estimator

scholarly journals SEMIPARAMETRIC ESTIMATION WITH GENERATED COVARIATES

2015 ◽  
Vol 32 (5) ◽  
pp. 1140-1177 ◽  
Author(s):  
Enno Mammen ◽  
Christoph Rothe ◽  
Melanie Schienle
Keyword(s):  
Nonlinear Models ◽  
Asymptotic Variance ◽  
Asymptotic Properties ◽  
Control Variable ◽  
Semiparametric Estimation ◽  
Nuisance Parameters ◽  
Infinite Dimensional ◽  
Asymptotically Normal ◽  
Endogenous Covariates ◽  
Nonstandard Problem

We study a general class of semiparametric estimators when the infinite-dimensional nuisance parameters include a conditional expectation function that has been estimated nonparametrically using generated covariates. Such estimators are used frequently to e.g., estimate nonlinear models with endogenous covariates when identification is achieved using control variable techniques. We study the asymptotic properties of estimators in this class, which is a nonstandard problem due to the presence of generated covariates. We give conditions under which estimators are root-nconsistent and asymptotically normal, derive a general formula for the asymptotic variance, and show how to establish validity of the bootstrap.

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