On the Asymptotic Effect of Substituting Estimators for Nuisance Parameters in Inferential Statistics

• Main Authors: YANG, Zhenlin, TSE, Yiu Kuen, BAI, Zhidong
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2003
• Subjects: Analytical correction; asymptotic independence; classical inference; limiting distribution; nuisance parameter; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/685; https://ink.library.smu.edu.sg/context/soe_research/article/1684/viewcontent/Yang_Tse_Bai.pdf
• Institution: Singapore Management University

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.