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EnglishThe covariance between the estimator and the score must be a linear transformation of the Fisher information matrix. It has been shown that this is a necessary and sufficient condition for the existence of a finite Cramér-Rao bound. In this note we show that this condition is unnecessary to obtain the above bound if the matrix of the linear transformation is limited in norm. A unified approach based on the matrix of minimum norm enables us to obtain a meaningful Cramér-Rao bound with the regular inverse replaced by the Moore-Penrose pseudoinverse as suggested by several authors. In this case the lower bound is achieved if and only if the estimator is a (minimum norm) linear transformation of the score.
Some comments on the Cramér-Rao bound when the information matrix is singular / M.Barnabani. - In: FAR EAST JOURNAL OF THEORETICAL STATISTICS. - ISSN 0972-0863. - STAMPA. - Vol.31 Number 2(2010), pp. 97-106.
| Titolo: | Some comments on the Cramér-Rao bound when the information matrix is singular | |
| Autori di Ateneo: | ||
| Autori: | BARNABANI, MARCO | |
| Data di pubblicazione: | 2010 | |
| Rivista: | ||
| Volume: | Vol.31 Number 2 | |
| Pagina iniziale: | 97 | |
| Pagina finale: | 106 | |
| Abstract: | The covariance between the estimator and the score must be a linear transformation of the Fisher information matrix. It has been shown that this is a necessary and sufficient condition for the existence of a finite Cramér-Rao bound. In this note we show that this condition is unnecessary to obtain the above bound if the matrix of the linear transformation is limited in norm. A unified approach based on the matrix of minimum norm enables us to obtain a meaningful Cramér-Rao bound with the regular inverse replaced by the Moore-Penrose pseudoinverse as suggested by several authors. In this case the lower bound is achieved if and only if the estimator is a (minimum norm) linear transformation of the score. | |
| Handle: | http://hdl.handle.net/2158/389222 | |
| Appare nelle tipologie: | 1a - Articolo su rivista |
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