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On prediction and mean squared error
Author(s) -
Yatracos Yannis G.
Publication year - 1992
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315467
Subject(s) - mathematics , mean squared error , extension (predicate logic) , mean square , cover (algebra) , type (biology) , statistics , function (biology) , econometrics , computer science , engineering , mechanical engineering , ecology , evolutionary biology , biology , programming language
Practical questions motivate the search for predictors either of an as yet unobserved random vector, or of a random function of a parameter. An extension of the classical UMVUE theory is presented to cover such situations. In includes a Rao‐Blackwell‐type theorem, a Cramer‐Rao‐type inequality, and necessary and sufficient conditions for a predictor to minimize the mean squared error uniformly in the parameter. Applications are considered to the problem of selected means, the species problem, and the examination of some u‐v estimates of Robbins (1988).