Second-order Accurate Confidence Regions Based on Members of the Generalized Power Divergence Family

2015 ◽  
Vol 43 (1) ◽  
pp. 213-227 ◽  
Author(s):  
Nicola Lunardon ◽  
Gianfranco Adimari
Keyword(s):  
Confidence Regions ◽  
Second Order ◽  
Power Divergence

On Second Order Efficiency of Minimum Discrepancy and Minimum Distance Estimators for the Multinomial Distribution

1988 ◽  
Vol 37 (1-2) ◽  
pp. 17-28 ◽  
Author(s):  
B. N. Nagnur ◽  
M.S. Hegde
Keyword(s):  
Minimum Distance ◽  
Multinomial Distribution ◽  
Second Order ◽  
Distance Functions ◽  
Asymptotically Normal ◽  
Minimum Discrepancy ◽  
Second Order Efficiency ◽  
Minimum Distance Estimators ◽  
Power Divergence ◽  
Asymptotically Efficient

Rao (1961, '62, '63) introduced the concept of second order efficiency (s.o.e.) of an asymptotically efficient i.e., best asymptotically normal (BAN) estimator. The main purpose of introducing this concept was to discriminate different asymptotically efficient estimators. Rao considered some wellknown methods of estimation for the multinomial distribution with true cell probabilities depending on a single unknown parameter. Nagnur and Aithal (1986) obtained a general expression for the s.o.e. of minimum distance estimators, obtained from a particular form of a distance function given by Taylor (1953) for the multinomial distribution . In this paper we have obtained the expression for the s.o.e. of minimum discrepancy (minimum power-divergence) estimators, obtained from a discrepancy function defined by Cressie and Read (1984) . The distance functions and the discrepancy functions which produce estimators having the same s.o.e. have been identified.

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

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