For the multi-parameter discrete exponential family,we construct an empirical Bayes(EB)estimator of the vector-valued parameterθ.under some conditions,this estimator is proved to be asymptotically optimal.
Thek-dimensional Piatetski-Shapiro prime number problem fork?3 is studied. Let π(x 1 c 1,?,c k ) denote the number of primesp withp?x, $p = [n_1^{c_1 } ] = \cdots [n_k^{c_k } ]$ , where 1<c 1<?<c k are fixed...Thek-dimensional Piatetski-Shapiro prime number problem fork?3 is studied. Let π(x 1 c 1,?,c k ) denote the number of primesp withp?x, $p = [n_1^{c_1 } ] = \cdots [n_k^{c_k } ]$ , where 1<c 1<?<c k are fixed constants. It is proved that π(x;c 1,?,c k ) has an asymptotic formula ifc 1 ?1 +?+c k ?1 >k?k/(4k 2+2).展开更多
文摘For the multi-parameter discrete exponential family,we construct an empirical Bayes(EB)estimator of the vector-valued parameterθ.under some conditions,this estimator is proved to be asymptotically optimal.
基金Project supported by the National Natural Science Foundation of China (Grant No. 19801021)the Natural Science Foundation of Shandong Province (Grant No. Q98A02110).
文摘Thek-dimensional Piatetski-Shapiro prime number problem fork?3 is studied. Let π(x 1 c 1,?,c k ) denote the number of primesp withp?x, $p = [n_1^{c_1 } ] = \cdots [n_k^{c_k } ]$ , where 1<c 1<?<c k are fixed constants. It is proved that π(x;c 1,?,c k ) has an asymptotic formula ifc 1 ?1 +?+c k ?1 >k?k/(4k 2+2).
