Publication Type
Journal Article
Version
publishedVersion
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
Citation
YANG, Zhenlin; TSE, Yiu Kuen; and Bai, Zhidong.
Statistics with Estimated Parameters. (2007). Statistica Sinica. 17, 817-837.
Available at: https://ink.library.smu.edu.sg/soe_research/434
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
http://www3.stat.sinica.edu.tw/statistica/J17N2/J17N220/J17N220.html