Asymptotic Second-Order Efficiency for Multivariate Two-Stage Estimation of a Linear Function of Normal Mean Vectors

2004 ◽  
Vol 23 (3) ◽  
pp. 333-353 ◽  
Author(s):  
Makoto Aoshima ◽  
Yoshikazu Takada
Keyword(s):  
Linear Function ◽  
Second Order ◽  
Two Stage ◽  
Normal Mean ◽  
Second Order Efficiency ◽  
Mean Vectors ◽  
Stage Estimation

Estimation of location parameter within pre-specified error bound with second-order efficient two-stage procedure

2021 ◽  
Vol 55 (1) ◽  
pp. 45-54
Author(s):  
Bhargab Chattopadhyay ◽  
Swarnali Banerjee
Keyword(s):  
Confidence Interval ◽  
Nuisance Parameter ◽  
Location Parameter ◽  
Second Order ◽  
Two Stage ◽  
Absolute Deviation ◽  
Asymptotic Consistency ◽  
Efficiency Property ◽  
Normal Mean ◽  
Optimality Properties

This paper develops a general approach for constructing a confidence interval for a parameter of interest with a specified confidence coefficient and a specified width. This is done assuming known a positive lower bound for the unknown nuisance parameter and independence of suitable statistics. Under mild conditions, we develop a modified two-stage procedure which enjoys attractive optimality properties including a second-order efficiency property and asymptotic consistency property. We extend this work for finding a confidence interval for the location parameter of the inverse Gaussian distribution. As an illustration, we developed a modified mean absolute deviation-based procedure in the supplementary section for finding a fixed-width confidence interval for the normal mean.

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