In statistical inference one of the most important properties that an estimator of an unknown parameter can possess is the property of sufficiency. The use of sufficient statistics has been prescribed in the past and their use today plays an ever increasing role in modern statistical inference. Because of the utmost importance of sufficient statistics, it is the goal of this thesis to study the various aspects of sufficiency in connection with the estimation of parameters.This study utilizes a blend of a geometric and an analytic approach to sufficiency. This is done to show the power of each and to demonstrate how the two approaches complement each other and combine to give better insight into the concept of sufficiency.In this thesis the author also establishes some new and important results on sufficiency and minimal sufficiency. These results, taken as a whole, constitute a unified presentation of some of the most important aspects of sufficiency and non-sufficiency.
| Identifer | oai:union.ndltd.org:BSU/oai:cardinalscholar.bsu.edu:handle/181227 |
| Date | January 1976 |
| Creators | Bookmyer, Lloyd D. |
| Contributors | Ali, Mir M. |
| Source Sets | Ball State University |
| Detected Language | English |
| Format | 61 leaves ; 28 cm. |
| Source | Virtual Press |
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