Wichita State University
Suppose that X is random variable with distribution function F. X and F are said to be symmetric if X and -X have the same distribution, i.e., F has a positive Type II bias if is increasing in
It is known that the Maximum Likelihood Estimator of F under the constraint of Type II bias is inconsistent if F is continuous. We introduce a projection type estimator, show that it is uniformly consistent almost surely, and derive its weak convergence (a functional CLT) properties for dawing statistical inference.
In competing risks problems with two causes of failure (e.g., heart disease and cancer competing to kill you) one defines the cumulative incidence functions by where T is the lifetime and is the cause. Note that One model for disease 2 being deadlier than 1 is is increasing in The mathematical structure of this problem is the same as that of the first one, and all results can be borrowed w/o any changes. Also considered is random right censoring, e.g. when one decides to move out of a study or gets run over by a truck before either disease gets her.
Please join us for refreshments before the lecture at 2:30p.m. in room 353 Jabara Hall.
[ Fall 2001]