ruth@utstat.uucp (Ruth Croxford) (02/07/89)
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ruth@utstat.uucp (Ruth Croxford) (02/07/89)
Topic: Marginal tail area approximations in multi-variable problems Speaker: Chris Field, Dept of Math, Stats & Comp Sci, Dalhousie University Date: 4:00 p.m., February 10, 1989 Place: room 2110, Sidney Smith Hall, 100 St George St, University of Toronto Abstract: In many statistical problems, it is important to be able to compute tail areas accurately. We present a tail area approximation for the mean developed by Lugannani and Rice. We show how it can be viewed as a local normal approx- imation after embedding the underlying density in an appropriate exponential family. The results are extended to multi-variable situations in which the density of statistics is proportional to exp(1(x)) where 1(x) is known and the distribution function of one of the statistics is to be approximated. Condi- tional inference about the parameters of a multiple regression problem fall into this category. We present the appropriate tail area approximation required to compute conditional confidence intervals for a single parameter of interest. Numerical results for some common location/scale models show excel- lent agreement between exact and approximate areas for samples of size 5 with 2 of these being type 2 censored. Some preliminary numerical results for mul- tiple regression will also be given. ----------- Coffee and tea will be served in the DeLury Lounge (SS6006) at 3:30 p.m.