**Prof. Hari Mukerjee**

Wichita State University

**"Consistent Estimation of Distributions with Type II Bias with Applications in Competing Risks Problems"**

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.

#### Friday, September 14, 2001

3:00 PM in 335 Jabara Hall

Please join us for refreshments before the lecture at 2:30p.m. in room 353 Jabara Hall.

[ Fall 2001]