OPTIMAL UNBIASED STATISTICAL ESTIMATING FUNCTIONS FOR HILBERT-SPACE VALUED PARAMETERS

被引：2
作者：
SUBRAMANYAM, A
NAIKNIMBALKAR, UV
机构：
[1] INDIAN INST TECHNOL,DEPT MATH,BOMBAY 400076,INDIA
[2] UNIV POONA,DEPT STAT,POONA 411007,MAHARASHTRA,INDIA
来源：
JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 1990年 / 24卷 / 01期
关键词：
complete orthonormal basis; Cramér-Rao inequality; interesting and nuisance Hilbert space valued parameters; score function;
D O I：
10.1016/0378-3758(90)90020-U
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
An extended Cramér-Rao type inequality is shown to hold for unbiased statistical estimating functions (USEFs) when the parameter space is a real separable Hilbert space. This enables a definition of an 'optimality criterion' for the USEFs. A definition of the score function is given in this set up and it is shown that the USEF based on it is optimal. A bound is also obtained in the presence of nuisance parameters. Finally some examples are given. © 1990.
引用
收藏
页码：95 / 105
页数：11
相关论文
共 13 条
[1]   NONPARAMETRIC INFERENCE FOR A FAMILY OF COUNTING PROCESSES [J].
AALEN, O .
ANNALS OF STATISTICS, 1978, 6 (04) :701-726
[2]   A SIEVE ESTIMATOR FOR THE MEAN OF A GAUSSIAN PROCESS [J].
BEDER, JH .
ANNALS OF STATISTICS, 1987, 15 (01) :59-78
[3]  
Bhapkar V. P., 1972, SANKHYA A, V34, P467
[4]   UNBIASED STATISTICAL ESTIMATION FUNCTIONS FOR PARAMETERS IN PRESENCE OF NUISANCE PARAMETERS [J].
CHANDRASEKAR, B ;
KALE, BK .
JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 1984, 9 (01) :45-54
[5]  
CHANDRASEKAR B, 1983, THESIS U POONA INDIA
[6]   MULTIPARAMETRIC ESTIMATING EQUATIONS [J].
FERREIRA, PE .
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 1982, 34 (03) :423-431
[7]  
GODAMBE VP, 1985, BIOMETRIKA, V72, P419
[8]   AN OPTIMUM PROPERTY OF REGULAR MAXIMUM-LIKELIHOOD ESTIMATION [J].
GODAMBE, VP .
ANNALS OF MATHEMATICAL STATISTICS, 1960, 31 (04) :1208-1211
[9]  
Grenander U, 1980, ABSTRACT INFERENCE
[10]  
HASMINSKII RZ, 1980, LECT NOTES CONTROL I, V0025, P00001
12