Estimating the Correlation Coefficient for Censored Data via Maximum Likelihood

Undergraduate #71
Discipline: Mathematics and Statistics
Subcategory:

Isaac Wright - Savannah State University
Co-Author(s): Alexander Giessing, University of Michigan, Ann Arbor, MI

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When data collection instruments have a detection limit, values above or below this limit are unobservable resulting in the value being recorded at the limit. These values are called ‘censored’. Unless the censoring is accounted for, inference on the censored values is biased due to the loss of information. In this study, we are interested in estimating the correlation between variables from the bivariate normal distribution with right censoring. To estimate the correlation we use the maximum likelihood approach. We derive the likelihood and implement the maximum likelihood estimation in R using the general-purpose optimizer ‘optim’. To assess the accuracy of our procedure we do simulation studies with varying sample sizes, different censoring levels, and changes to the underlying correlation. Through these simulations we illustrate the effectiveness of our method and show that it outperforms the naive estimation procedure. We also apply our method to the well-known Galton data set. This data set contains the heights of both parents and children. We estimate the correlation between heights of parents and sons after censoring the data.

Funder Acknowledgement(s): Rackham Graduate School , University of Michigan

Faculty Advisor: Xuming He, xmhe@umich.edu

Role: My role consisted of several parts. First, I derived the function for our specific problem. Then I coded the function in R software and tested it through large scale simulations. After finding the function produced accurate results, I extended it by applying the code to a real data set.