scholarly journals Second order efficiency

Scholarpedia ◽  
2009 ◽  
Vol 4 (3) ◽  
pp. 7084
Author(s):  
Calyampudi Rao
Keyword(s):  
Second Order ◽  
Second Order Efficiency

Edgeworth Expansions for Fisher­Consistent Estimators and Second Order Efficiency

1979 ◽  
Vol 28 (1-4) ◽  
pp. 1-18
Author(s):  
J. K. Ghosh ◽  
Bimal Kumar Sinha ◽  
K. Subramanyam
Keyword(s):  
Recent Result ◽  
Lebesgue Measure ◽  
Loss Function ◽  
Exponential Family ◽  
Second Order ◽  
Probability Inequality ◽  
Edgeworth Expansions ◽  
Second Order Efficiency ◽  
Curved Exponential Family

Using a recent result of Bhattacharya, R. N. and Ghosh, J. K. ( Annals of Statistics, 1978, 434­451), Edgeworth expansions of distributions of Fisherconsistent estimators for curved exponential family of parent distributions (dominated by the Lebesgue measure) can be obtained. We compare directly the first four cumulants of an arbitrary Fisher­consistent estimator with those of the MLE after correcting them for their bias. This leads to a key probability inequality which immediately implies the second order efficiency of the MLE wrt any bounded bowl­ shaped loss function. If the assumption of a dominating Lebesgue measure is dropped the formal Edgeworth expansions are no longer valid. However it turns out that if the loss function satisfies certain additional conditions the second order efficiency of the MLE holds. This modification takes care of the curved multinomial.

scholarly journals Penalized maximum likelihood and semiparametric second-order efficiency

2006 ◽  
Vol 34 (1) ◽  
pp. 169-201 ◽  
Author(s):  
A. S. Dalalyan ◽  
G. K. Golubev ◽  
A. B. Tsybakov
Keyword(s):  
Maximum Likelihood ◽  
Second Order ◽  
Penalized Maximum Likelihood ◽  
Second Order Efficiency
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