Admissibility of Confidence Estimators in the Regression Model
In the regression model, we assume that the independent variables are random instead of fixed. Consider the problem of estimating the coverage function of a usual confidence interval for the unknown intercept parameter. In this paper, we consider a case in which the number of unknown parameters is s...
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| Veröffentlicht in: | Journal of multivariate analysis Jg. 76; H. 2; S. 267 - 276 |
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| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
San Diego, CA
Elsevier Inc
01.02.2001
Elsevier |
| Schriftenreihe: | Journal of Multivariate Analysis |
| Schlagworte: | |
| ISSN: | 0047-259X, 1095-7243 |
| Online-Zugang: | Volltext |
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| Abstract | In the regression model, we assume that the independent variables are random instead of fixed. Consider the problem of estimating the coverage function of a usual confidence interval for the unknown intercept parameter. In this paper, we consider a case in which the number of unknown parameters is smaller than 5. We show that the usual constant coverage probability estimator is admissible in the usual sense in this case. Note that this estimator is inadmissible in the usual sense in the other case where the number of unknown parameters is greater than 4. |
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| AbstractList | In the regression model, we assume that the independent variables are random instead of fixed. Consider the problem of estimating the coverage function of a usual confidence interval for the unknown intercept parameter. In this paper, we consider a case in which the number of unknown parameters is smaller than 5. We show that the usual constant coverage probability estimator is admissible in the usual sense in this case. Note that this estimator is inadmissible in the usual sense in the other case where the number of unknown parameters is greater than 4. |
| Author | Wang, Hsiuying |
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| Copyright | 2001 Academic Press 2001 INIST-CNRS |
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| Keywords | confidence interval, admissibility, coverage function, the usual coverage probability estimator, ancillary statistic Admissibility Parameter estimation Admissible estimator Statistical theory Confidence limit Non parametric estimation Tolerance limit Statistical estimation Statistical decision Independent variable Confidence interval Statistical regression Regression model Decision theory Bayes decision Random variable |
| Language | English |
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| References | Wang (RF4) 1998; 36 Brown (RF1) 1990; 18 Wang (RF3) 1999; 27 Brown, Gene Hwang (RF2) 1990 Brown (10.1006/jmva.2000.1912_RF1) 1990; 18 Wang (10.1006/jmva.2000.1912_RF3) 1999; 27 Wang (10.1006/jmva.2000.1912_RF4) 1998; 36 Brown (10.1006/jmva.2000.1912_RF2) 1990 |
| References_xml | – volume: 27 start-page: 610 year: 1999 end-page: 626 ident: RF3 article-title: Brown's paradox in the estimated confidence approach publication-title: Ann. Statist. – year: 1990 ident: RF2 article-title: Admissibility of confidence estimators publication-title: Proceedings of 1990 Taipei Symposium in Statistics – volume: 18 start-page: 471 year: 1990 end-page: 538 ident: RF1 article-title: An ancillarity paradox which appears in multiple linear regression (with discussion) publication-title: Ann. Statist. – volume: 36 start-page: 365 year: 1998 end-page: 372 ident: RF4 article-title: Admissibility of the constant coverage probability estimator for estimating the coverage function of certain confidence interval publication-title: Statist. Probab. Lett. – year: 1990 ident: 10.1006/jmva.2000.1912_RF2 article-title: Admissibility of confidence estimators – volume: 36 start-page: 365 year: 1998 ident: 10.1006/jmva.2000.1912_RF4 article-title: Admissibility of the constant coverage probability estimator for estimating the coverage function of certain confidence interval publication-title: Statist. Probab. Lett. doi: 10.1016/S0167-7152(97)00083-7 – volume: 18 start-page: 471 year: 1990 ident: 10.1006/jmva.2000.1912_RF1 article-title: An ancillarity paradox which appears in multiple linear regression (with discussion) publication-title: Ann. Statist. doi: 10.1214/aos/1176347602 – volume: 27 start-page: 610 year: 1999 ident: 10.1006/jmva.2000.1912_RF3 article-title: Brown's paradox in the estimated confidence approach publication-title: Ann. Statist. doi: 10.1214/aos/1018031210 |
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| SubjectTerms | admissibility ancillary statistic confidence interval confidence interval, admissibility, coverage function, the usual coverage probability estimator, ancillary statistic coverage function Decision theory Exact sciences and technology Mathematics Nonparametric inference Parametric inference Probability and statistics Sciences and techniques of general use Statistics the usual coverage probability estimator |
| Title | Admissibility of Confidence Estimators in the Regression Model |
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