Minimax-linear estimation under incorrect prior information. (English) Zbl 0594.62063
Robustness of statistical methods and nonparametric statistics, Pap. Conf., Schwerin/Mecklenb. 1983, Theory Decis. Libr., Ser. B 1, 156-158 (1984).
Summary: [For the entire collection see Zbl 0588.00027.]
If nonlinear prior information on the parameter \(\beta\) of the familiar linear regression model is available such that \(\beta\) may be assumed to be in a convex set (a concentration ellipsoid), then this information is used optimally by a minimax estimator (MILE). The MILE is of ridge type and is of smaller minimax risk compared with the BLUE so far the prior information is true. The MILE is said to be insensitive against misspecifications of the prior region if its risk stays smaller than the risk of the BLUE. Necessary and sufficient conditions are given for the insensitivity of MILE in typical situations of incorrect prior information.
If nonlinear prior information on the parameter \(\beta\) of the familiar linear regression model is available such that \(\beta\) may be assumed to be in a convex set (a concentration ellipsoid), then this information is used optimally by a minimax estimator (MILE). The MILE is of ridge type and is of smaller minimax risk compared with the BLUE so far the prior information is true. The MILE is said to be insensitive against misspecifications of the prior region if its risk stays smaller than the risk of the BLUE. Necessary and sufficient conditions are given for the insensitivity of MILE in typical situations of incorrect prior information.
MSC:
| 62H12 | Estimation in multivariate analysis |
