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Approximation to the moments of ratios of cumulative sums
Author(s) -
Shi Xiaoping,
Reid Nancy,
Wu Yuehua
Publication year - 2014
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 - 10.1002/cjs.11213
Subject(s) - mathematics , statistics , sequence (biology) , random variable , kernel (algebra) , term (time) , point (geometry) , regression analysis , econometrics , combinatorics , physics , genetics , quantum mechanics , biology , geometry
Abstract We propose an approximation to the mean of the ratio of cumulative sums of a sequence of independently distributed nonnegative random variables. Both leading term and higher‐order saddlepoint approximations are presented, and the results are applied to a vector ratio approximation, change‐point analysis, and kernel regression. The Canadian Journal of Statistics 42: 325–336; 2014 © 2014 Statistical Society of Canada