is increasing in 
Wichita State University
Abstract:
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]