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On The Asymptotic Effect Of Substituting Estimators For Nuisance Parameters In Inferential Statistics, Zhenlin Yang, Yiu Kuen Tse, Zhidong Bai

Research Collection School Of Economics

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 …