ISSN:
1432-2064
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary For n=1,2, ... let P n be a set of probability measures on the measurable space (X, A) containing a fixed nulldistribution P 0. We study approximations of P n n ={P n : P∈P n } for large n. Degeneracy is avoided by postulating that (1) no P n can be distinguished from P 0 n with probability almost 1 (P∈P n ); (2) events of small P 0-probability contain little information. The second condition turns out to be equivalent to the existence of nondegenerating multinomial approximations to P n n obtained from partitions of the sample space X. In particular we consider the case that (X, A) is the real axis endowed with the field of Borel sets and that dP/dP 0 (x) are monotonic functions of x. If (1) and (2) are satisfied, the family P n n can be approximated by a multinomial family obtained from an interval partition of the line which depends on the accuracy of approximation, but not on n.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00533639
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