Publication Type
Working Paper
Version
publishedVersion
Publication Date
6-2003
Abstract
This paper studies the general problem of making inferences for a set of parameters ? in the presence of another set of (nuisance) parameters λ, based on the statistic T(y; ˆλ, θ), where y = {y1, y2, · · · , yn} represents the data, ˆλ is an estimator of λ and the limiting distribution of T(y; λ, θ) is known. We provide general methods for finding the limiting distributions of T(y; ˆλ, θ) when ˆλ is either a constrained estimator (given θ) or an unconstrained estimator. The methods will facilitate hypothesis testing as well as confidence-interval construction. We also extend the results to the cases where inferences may concern a general function of all parameters (θ and λ) and/or some weakly exogenous variables. Applications of the theories to testing serial correlation in regression models and confidence-interval construction in Box-Cox regressions are given.
Keywords
Analytical correction, asymptotic independence, classical inference, limiting distribution, nuisance parameter
Discipline
Econometrics
Research Areas
Econometrics
Volume
13-2003
First Page
1
Last Page
15
Publisher
SMU Economics and Statistics Working Paper Series, No. 1032003
City or Country
Singapore
Citation
YANG, Zhenlin; TSE, Yiu Kuen; and BAI, Zhidong.
On the Asymptotic Effect of Substituting Estimators for Nuisance Parameters in Inferential Statistics. (2003). 13-2003, 1-15.
Available at: https://ink.library.smu.edu.sg/soe_research/685
Copyright Owner and License
Authors
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.