An Algorithm In Decision Fusion System And A Kind Of Pickands-type Estimator For The Extreme Value Index

It is well-known that the multisensor data fusion techniques have receivedsignificant attention for both military and non-military applications. One of theprimary problems in the multisensor data fusion is distributed multisensor deci-sion problem that was first formulated by Tenney and Sandell in 1980s'. Theystudied two-sensor Bayes binary decision problem under a given fusion rule withindependent sensor observations cross sensors. For the multisensor distributeddecision problem, two fundamental issues are how to compute optimal local sen-sor compression rules with general (dependent) sensor observations given a fixedfusion rule and search for an optimal fusion rule. Many researchers devotedthemselves to the work for the optimal fusion rule problem and the optimal localcompression rule issue. An optimal fusion rule was presented for a special com-munication pattern in the publications. For general multisensor decision fusionsystem, the optimal fusion rule problem is still an open question. In this paper,an algorithm is obtained to search for an optimal fusion rule and the correspond-ing optimal local sensor compression rules simultaneously. However, it is wellknown that to determine an optimal fusion rule, usually one needs to exhaus-tively compare all possible fusion rules and their decision costs after calculatingthe corresponding sensor rules. The fusion center of the original decision systemis regarded as a suppositional local sensor. Thereby, the problem on the optimalfusion rule and corresponding optimal local sensor rules for the original systemis converted into a problem on optimal local sensor compression rules under agiven fusion rule for the system with a suppositional local sensor. The neces-sary condition for optimal sensor rules is presented in the aforementioned newsystem. The finite convergence of the discretized algorithm is also proved. Nu- merical examples show the efficiency of the proposed algorithm.Classical extreme value theory is concerned substantially with asymptoticdistributional property of maximum (or minimum) of n independent and iden-tically distributed random variables, as n becomes large. It has become a sig-nificant branch of probability theory. There are many engineering areas whereextreme value theory plays a decisive role. These fields include ocean and envi-ronmental engineering, meteorology, traffic engineering, hydraulics engineering,etc. It plays an important role in economics, too. In applications of the extremevalue theory, it is necessary to estimate the probability distribution of rare eventssuch as the maximum earthquake intensity, the largest waves, large insuranceclaims, etc. And these estimators are linked with the extreme value index. Thequestion is how to estimate the extreme value index from a sample. Of course,there are some methods to estimate the extreme value index. Most of such pub-lications are based on the work of Pickands III and Hill. For example, a newPickands-type estimator, a location invariant Hill-type estimator and moment es-timator were proposed to estimate the extreme value index. Estimators for a largequantile and for the upper endpoint of a distribution are obtained which based ona new Pickands-type estimator, which once proposed by the author. Furthermorethe asymptotic properties of these estimator are discussed in this thesis.Regardless of the estimator for the extreme value index (Pickands-type es-timator, Hill-type estimator or moment estimator) or the estimator for the largequantile and the upper endpoint, these estimators are based on sample (orderstatistics). Therefor, the problem on the optimal choice for the number of upperorder statistics in estimation of the extreme value index is vary important. Anasymptotic expansion is obtained under regular variation condition. Moreover,a method to choose the asymptotically optimal number of upper order statisticsinvolved in estimation of the extreme value index is presented in this thesis.