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Title: Estimation of two-dimensional rate functions using incomplete data Authors:  Micha Mandel - The Hebrew University of Jerusalem (Israel) [presenting]
Naomi Kaplan-Damary - The Hebrew University of Jerusalem (Israel)
Yoram Yekutieli - Hadassah Academic College (Israel)
Sarena Wiesner - Israel National Police (Israel)
Yaron Shor - Israel National Police (Israel)
Abstract: A sample of two-dimensional counting processes having a joint rate function up to a multiplicative constant is considered. The points of each process can be observed only in a process-specific set, leading to truncated data. The aim is to estimate non-parametrically the rate function. We discuss several estimation methods based on mixed logistic and Poisson models and on conditional likelihood. As the approaches are computationally expensive and the number of points in each process is small, case-control sampling is used to reduce the computation effort. The problem is motivated by forensic footwear analysis that is based on randomly acquired characteristics found in the shoe sole. The methods will be demonstrated using a large dataset collected by the Division of Identification and Forensic Science of the Israeli National Police.