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Consistency of least‐squares estimator and its jackknife variance estimator in nonlinear models
Author(s) -
Shao Jun
Publication year - 1992
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315611
Subject(s) - jackknife resampling , mathematics , estimator , consistency (knowledge bases) , statistics , non linear least squares , consistent estimator , minimum variance unbiased estimator , bias of an estimator , nonlinear regression , generalized least squares , econometrics , regression analysis , geometry
The purpose of this paper is twofold: (1) We establish the consistency of the least‐squares estimator in a nonlinear modely i = f(x i ,θ) +σ i e i where the range of the parameter θ is noncompact, the regression function is unbounded, and the σ i ,'s are not necessarily equal. This extends the results in Jennrich (1969) and Wu (1981). (2) Under the same model, the jackknife estimator of the asymptotic covariance matrix of the least‐squares estimator is shown to be consistent, which provides a theoretical justification of the empirical results in Duncan (1978) and the use of the jackknife method in large‐sample inferences.