The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
Fisher’s (Proceedings of Royal Society Series A 144, 285–307 1934, 1956) example remains a classic where the maximum likelihood estimator (T) was non-sufficient, had less than full information, but an ancillarity complement (S) helped in recovering the full information I ( T , S ) ( 𝜃 ) $\mathcal {I}_{(T,S)}(\theta )$ . In the absence of other readily accessible easy-to-grasp examples...
D. Basu gave a striking bivariate normal example, N2(0, 0, 1, 1, ρ) with an unknown correlation coefficient ρ, − 1 < ρ < 1, where the jointly sufficient statistic (X1, X2) consists of two ancillary statistics X1, X2. We exhibit examples of ancillary statistics involving both X1, X2 followed by other variations. A situation is highlighted where a jointly minimal sufficient statistic (X...
Misconceptions are many when it comes to Fisher information, sufficiency, and ancillarity, especially among beginners. Many believe that $$\mathcal I _{T_{1}}(\theta )+\mathcal I _{T_{2}}(\theta )$$ should equal $$\mathcal I _{T_{1}+T_{2}}(\theta )$$ for all $$\theta $$ . We exhibit precise scenarios where $$\mathcal I _{T_{1}+T_{2}}(\theta )$$ is $$<, =,$$ or $$>\mathcal...
Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.