Inferential Methods for Censored Bivariate Normal Data
ABSTRACT:
The Expectation-Maximization (EM) algorithm is a useful tool to
estimate the parameters of the distribution based on incomplete data,
especially when the complete data problems are relatively easy. The
Type-II right censored or progressively Type-II right censored
bivariate normal data can be viewed as an incomplete data and the EM
algorithm can then be applied to determine the MLEs of the parameters.
In this talk, I will first explain the application of the EM algorithm
to Type-II right censored bivariate normal data. Then, I will discuss
the MLEs of the parameters of a bivariate normal distribution based on
a progressively Type-II censored data. I will also discuss the interval
estimation of the parameters using the asymptotic variances and
covariances of the MLEs derived from the Fisher information matrix.
Sample-based Monte Carlo confidence intervals will be introduced to
improve the probability coverages of these asymptotic confidence
intervals. Next, the extension of the EM algorithm to progressively
Type-II right censored bivariate normal data will be discussed.
Finally, some illustrative examples will be presented.
About the Speaker
Jeong-Ae Kim is a PhD student at McMaster University. She is doing her
thesis on the topic of inference for censored bivariate data under the
supervision of Prof. N. Balakrishnan. Jeong-Ae plans to have her final
thesis defence in the summer of 2004.
References
Harrell, F. E. and Sen, P. K. (1979). Statistical inference for
censored bivariate normal distributions based on induced order
statistics, Biometrika, 66, 293-298.
Ng, H. K. T., Chan, P. S. and Balakrishnan, N. (2002). Estimation of
parameters from progressively censored data using EM algorithm, Computational
Statistics & Data Analysis, 39, 371-386.
