Edgeworth Expansion of the Parametric Bootstrap t-statistic for Linear Regression Processes with Strongly Dependent Errors
The purpose of this paper is to provide a valid Edgeworth expansion for the parametric bootstrap t-statistic of a linear regression process whose error terms are stationary, Gaussian, and strongly dependent time series. Under some sets of conditions on the spectral density function and the parametri...
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| Format: | Article |
| Language: | English |
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Springer
2015-03-01
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| Series: | Journal of Statistical Theory and Applications (JSTA) |
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| Online Access: | https://www.atlantis-press.com/article/18187.pdf |
| _version_ | 1828364630008791040 |
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| author | Mosisa Aga |
| author_facet | Mosisa Aga |
| author_sort | Mosisa Aga |
| collection | DOAJ |
| description | The purpose of this paper is to provide a valid Edgeworth expansion for the parametric bootstrap t-statistic of a linear regression process whose error terms are stationary, Gaussian, and strongly dependent time series. Under some sets of conditions on the spectral density function and the parametric values, an Edgeworth expansion of the bootstrap t-statistic of arbitrarily large order of the process is proved to have an error of o(n1-s/2) where s is a positive integer. The result is similar to the Edgeworth expansion obtained by Andrews and Lieberman [2002], which was established for the parametric bootstrap t-statistic of the plug-in maximum likelihood (PML) estimators of stationary, Gaussian, and strongly dependent processes, but without the linear regression component. |
| first_indexed | 2024-04-14T05:19:50Z |
| format | Article |
| id | doaj.art-a70a986ccf3a46d692f83366b4daeb98 |
| institution | Directory Open Access Journal |
| issn | 1538-7887 |
| language | English |
| last_indexed | 2024-04-14T05:19:50Z |
| publishDate | 2015-03-01 |
| publisher | Springer |
| record_format | Article |
| series | Journal of Statistical Theory and Applications (JSTA) |
| spelling | doaj.art-a70a986ccf3a46d692f83366b4daeb982022-12-22T02:10:15ZengSpringerJournal of Statistical Theory and Applications (JSTA)1538-78872015-03-0114110.2991/jsta.2015.14.1.5Edgeworth Expansion of the Parametric Bootstrap t-statistic for Linear Regression Processes with Strongly Dependent ErrorsMosisa AgaThe purpose of this paper is to provide a valid Edgeworth expansion for the parametric bootstrap t-statistic of a linear regression process whose error terms are stationary, Gaussian, and strongly dependent time series. Under some sets of conditions on the spectral density function and the parametric values, an Edgeworth expansion of the bootstrap t-statistic of arbitrarily large order of the process is proved to have an error of o(n1-s/2) where s is a positive integer. The result is similar to the Edgeworth expansion obtained by Andrews and Lieberman [2002], which was established for the parametric bootstrap t-statistic of the plug-in maximum likelihood (PML) estimators of stationary, Gaussian, and strongly dependent processes, but without the linear regression component.https://www.atlantis-press.com/article/18187.pdfEdgeworth Expansion; parametric bootstrap; t-statisticlinear regressionstrongly dependent |
| spellingShingle | Mosisa Aga Edgeworth Expansion of the Parametric Bootstrap t-statistic for Linear Regression Processes with Strongly Dependent Errors Journal of Statistical Theory and Applications (JSTA) Edgeworth Expansion; parametric bootstrap; t-statistic linear regression strongly dependent |
| title | Edgeworth Expansion of the Parametric Bootstrap t-statistic for Linear Regression Processes with Strongly Dependent Errors |
| title_full | Edgeworth Expansion of the Parametric Bootstrap t-statistic for Linear Regression Processes with Strongly Dependent Errors |
| title_fullStr | Edgeworth Expansion of the Parametric Bootstrap t-statistic for Linear Regression Processes with Strongly Dependent Errors |
| title_full_unstemmed | Edgeworth Expansion of the Parametric Bootstrap t-statistic for Linear Regression Processes with Strongly Dependent Errors |
| title_short | Edgeworth Expansion of the Parametric Bootstrap t-statistic for Linear Regression Processes with Strongly Dependent Errors |
| title_sort | edgeworth expansion of the parametric bootstrap t statistic for linear regression processes with strongly dependent errors |
| topic | Edgeworth Expansion; parametric bootstrap; t-statistic linear regression strongly dependent |
| url | https://www.atlantis-press.com/article/18187.pdf |
| work_keys_str_mv | AT mosisaaga edgeworthexpansionoftheparametricbootstraptstatisticforlinearregressionprocesseswithstronglydependenterrors |