Publication Type

Journal Article

Version

Publisher’s Version

Publication Date

2007

Abstract

This paper studies a general problem of making inferences for functions of two sets of parameters where, when the first set is given, there exists a statistic with a known distribution. We study the distribution of this statistic when the first set of parameters is unknown and is replaced by an estimator. We show that under mild conditions the variance of the statistic is inflated when the unconstrained maximum likelihood estimator (MLE) is used, but deflated when the constrained MLE is used. The results are shown to be useful in hypothesis testing and confidence-interval construction in providing simpler and improved inference methods than do the standard large sample likelihood inference theories. We provide three applications of our theories, namely Box-Cox regression, dynamic regression, and spatial regression, to illustrate the generality and versatility of our results.

Keywords

Asymptotic distribution, finite sample performance, index parameter, variance deflation, variance inflation

Discipline

Econometrics | Economics

Research Areas

Econometrics

Publication

Statistica Sinica

Volume

17

First Page

817

Last Page

837

ISSN

1017-0405

Publisher

Academia Sinica

Creative Commons License

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.

Additional URL

http://www3.stat.sinica.edu.tw/statistica/J17N2/J17N220/J17N220.html

Included in

Econometrics Commons

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