The structure of higher order asymptotic theory of statistical estimation

2009 ◽  
pp. 175-197
Author(s):  
Masafumi Akahira
Keyword(s):  
Statistical Estimation ◽  
Asymptotic Theory ◽  
Higher Order

On the number of solutions of right-definite problems with a convergent Dirichlet integral

1982 ◽  
Vol 91 (3-4) ◽  
pp. 347-360 ◽  
Author(s):  
M. S. P. Eastham
Keyword(s):  
Differential Equations ◽  
Asymptotic Theory ◽  
Higher Order ◽  
The Other ◽  
Dirichlet Integral ◽  
Number Of Solutions ◽  
Linearly Independent ◽  
Higher Order Differential Equations

SynopsisA recently developed asymptotic theory of higher-order differential equations is applied to problems of right-definite type to determine the numbers M+, M− of linearly independent solutions with a convergent Dirichlet integral, M+ and M− referring to the usual upper and lower λ.-half-planes. Particular attention is given to the phenomenon noted by Karlsson in which one of M+ and M− is maximal but not the other. Conditions are given under which M+ (say) is maximal and M− is the same, one less, and two less.

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