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Stochastic Monotonicity and Conditioning in the Limit
Author(s) -
Nerman Olle
Publication year - 1998
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00121
Subject(s) - mathematics , monotonic function , limit (mathematics) , conditional probability distribution , sequence (biology) , stochastic ordering , conditional expectation , conditioning , combinatorics , discrete mathematics , pure mathematics , mathematical analysis , statistics , genetics , biology
Suppose that {( X n , Y n )} is a sequence of pairs of cector‐valued stochastic variables which converges weakly to ( X , Y ), and that { y n } converges to y . Sufficient conditions for the conditional distribution of X n given Y = y are given in terms of stochastic monotonicity. Conditions, which guarantee that also moments of the conditional distributions converge to the moments of the ones of the limit, are also derived.