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.

scholarly journals The Calculation of Velocity Constants for First- and Second-order Two-stage Reactions.

1950 ◽  
Vol 4 ◽  
pp. 1216-1220 ◽  
Author(s):  
Sigvard Wideqvist ◽  
Waclaw Szybalski ◽  
Niels Nielsen
Keyword(s):  
Second Order ◽  
Two Stage

Conditional likelihood and power: higher-order asymptotics

1992 ◽  
Vol 438 (1904) ◽  
pp. 433-446 ◽  
Keyword(s):  
Average Power ◽  
Nuisance Parameter ◽  
Second Order ◽  
Conditional Likelihood ◽  
Power Functions ◽  
Third Order ◽  
Contiguous Alternatives ◽  
Higher Order Asymptotics ◽  
Optimality Property ◽  
Lr Test

This paper considers, in the presence of a nuisance parameter, a very large class of tests that includes the conditional and the usual versions of the likelihood ratio (LR), Rao’s and Wald’s tests. Under contiguous alternatives and orthogonal parametrization, the power functions of the conditional and the usual versions of these tests have been compared and, in particular, it is seen that the power functions of the conditional versions, unlike those of the usual versions, are identical, up to the second-order, with the power functions of the corresponding tests with known nuisance parameter. An optimality property of the conditional LR test, in terms of second-order local maximinity, has been established. A test, optimal in the sense of third-order average power under contiguous alternatives, has been proposed. A weaker optimality property of Rao’s test, in terms of third-order average power, has also been indicated.

scholarly journals Two-Stage Stochastic Programming Scheduling Model for Hybrid AC/DC Distribution Network Considering Converters and Energy Storage System

2019 ◽  
Vol 10 (1) ◽  
pp. 181
Author(s):  
Peng Kang ◽  
Wei Guo ◽  
Weigang Huang ◽  
Zejing Qiu ◽  
Meng Yu ◽  
...  
Keyword(s):  
Wind Power ◽  
Reactive Power ◽  
Distribution Network ◽  
Stochastic Scheduling ◽  
Second Order ◽  
Mixed Integer ◽  
Two Stage ◽  
Dc Distribution ◽  
Scheduling Model ◽  
Second Order Cone

The development of DC distribution network technology has provided a more efficient way for renewable energy accommodation and flexible power supply. A two-stage stochastic scheduling model for the hybrid AC/DC distribution network is proposed to study the active-reactive power coordinated optimal dispatch. In this framework, the wind power scenario set is utilized to deal with its uncertainty in real time, which is integrated into the decision-making process at the first stage. The charging/discharging power of ESSs and the transferred active/reactive power by VSCs can be adjusted when wind power uncertainty is observed at the second stage. Moreover, the proposed model is transformed into a mixed integer second-order cone programming optimization problem by linearization and second-order cone relaxation techniques to solve. Finally, case studies are implemented on the modified IEEE 33-node AC/DC distribution system and the simulation results demonstrate the effectiveness of the proposed stochastic scheduling model and solving method.

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