Asymptotic results are obtained using an approach based on limit theorem results obtained for α-mixing sequences for the class of general spacings (GSP) methods which include the maximum spacings (MSP) method. The MS...Asymptotic results are obtained using an approach based on limit theorem results obtained for α-mixing sequences for the class of general spacings (GSP) methods which include the maximum spacings (MSP) method. The MSP method has been shown to be very useful for estimating parameters for univariate continuous models with a shift at the origin which are often encountered in loss models of actuarial science and extreme models. The MSP estimators have also been shown to be as efficient as maximum likelihood estimators in general and can be used as an alternative method when ML method might have numerical difficulties for some parametric models. Asymptotic properties are presented in a unified way. Robustness results for estimation and parameter testing results which facilitate the applications of the GSP methods are also included and related to quasi-likelihood results.展开更多
1 Main resultsSINCE the concept of complete convergence was raised by Hsu and Robbins （1947）, it has at- tracted much attention. The general results were proved by Baum and Katz （1965）: if{X<sub>n</sub>...1 Main resultsSINCE the concept of complete convergence was raised by Hsu and Robbins （1947）, it has at- tracted much attention. The general results were proved by Baum and Katz （1965）: if{X<sub>n</sub>,n≥1} is a sequence of i. i. d. random variables with EX<sub>n</sub>=0 E|X<sub>1</sub>|<sup>p</sup>【∞, p≥1, 1≥α】展开更多
A probability inequality for Sn and some pth moment (p≥2) inequalities for | Sn| and max 1≤k≤n |Sk|are established. Here Sn is the partial sum of a negatively associated sequence Based on these inequalities, a weak...A probability inequality for Sn and some pth moment (p≥2) inequalities for | Sn| and max 1≤k≤n |Sk|are established. Here Sn is the partial sum of a negatively associated sequence Based on these inequalities, a weak in variance principle for strictly stationary negatively associated sequences is proved under some general conditions展开更多
文摘Asymptotic results are obtained using an approach based on limit theorem results obtained for α-mixing sequences for the class of general spacings (GSP) methods which include the maximum spacings (MSP) method. The MSP method has been shown to be very useful for estimating parameters for univariate continuous models with a shift at the origin which are often encountered in loss models of actuarial science and extreme models. The MSP estimators have also been shown to be as efficient as maximum likelihood estimators in general and can be used as an alternative method when ML method might have numerical difficulties for some parametric models. Asymptotic properties are presented in a unified way. Robustness results for estimation and parameter testing results which facilitate the applications of the GSP methods are also included and related to quasi-likelihood results.
文摘1 Main resultsSINCE the concept of complete convergence was raised by Hsu and Robbins （1947）, it has at- tracted much attention. The general results were proved by Baum and Katz （1965）: if{X<sub>n</sub>,n≥1} is a sequence of i. i. d. random variables with EX<sub>n</sub>=0 E|X<sub>1</sub>|<sup>p</sup>【∞, p≥1, 1≥α】
基金Project supported by the National Natural Science Foundation of China,the Doctoral Program Foundation of the State Education Commission of China and the High Eductional Natural Science Foundation of Guangdong Province.
文摘A probability inequality for Sn and some pth moment (p≥2) inequalities for | Sn| and max 1≤k≤n |Sk|are established. Here Sn is the partial sum of a negatively associated sequence Based on these inequalities, a weak in variance principle for strictly stationary negatively associated sequences is proved under some general conditions
