GENERALIZED LEAST SQUARES ESTIMATION OF THE MEAN FUNCTION OF A COUNTING PROCESS BASED ON PANEL COUNTS

摘要

This paper considers nonparametric estimation of the mean function of a counting process based on periodic observations, i.e., panel counts. We present estimators derived through minimizing a class of generalized sums of squares subject to a monotonicity constraint. We establish consistency of the estimators and provide procedures to implement them with various weight functions. For specific weight functions, they reduce to the estimator given in , and are closely related to the nonparametric maximum likelihood estimator studied in . With other weight functions, the proposed estimators provide alternatives that can have better efficiency in non-Poisson situations than previous approaches. Simulations are used to examine the finite-sample performance of the proposed estimators.