TitleSaddle point approximation
NameLi, Jixin (author), Kolassa, John (chair), Xie, Minge (internal member), Hoover, Donald (internal member), Ohman-Strickland, Pamela (outside member), Rutgers University, Graduate School - New Brunswick,
SubjectStatistics and Biostatistics,
DescriptionWe extend known saddlepoint tail probability approximations to multivariate cases, including multivariate conditional cases. Our first approximation applies to both continuous and lattice variables, and requires the existence of a cumulant generating function. The method is applied to some examples, including a real data set from a case-control study of
endometrial cancer. The method contains less terms, is easier to implement than existing methods, and shows an accuracy comparable to that of existing methods. The drawback of the first method is that
the coefficient for the main term is not 1, and therefore it may be hard to show the reflexivity property which in general does not hold, because the route of path of the integral used in the saddlepoint method has to have positive real part. Our second method uses a different approach for the main term. We show that in the bivariate case, the reflexivity property holds. We applies the method to a three dimensional example, and our method demonstrates better accuracy than the normal approximation.
NoteIncludes bibliographical references (p. 60-61)
Noteby Jixin Li
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
RightsThe author owns the copyright to this work.