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This paper studies the general problem of making inferences for a set of parameters ? in the presence of another set of (nuisance) parameters ?, based on the statistic T(y; ˆ?, ?), where y = {y1, y2, · · · , yn} represents the data, ˆ? is an estimator of ? and the limiting distribution of T(y; ?, ?) is known. We provide general methods for finding the limiting distributions of T(y; ˆ?, ?) when ˆ? is either a constrained estimator (given ?) 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 (? and ?) 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.


Analytical correction, asymptotic independence, classical inference, limiting distribution, nuisance parameter



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Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

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