Statistica Sinica 19 (2009), 561-580

GENERALIZED LEAST SQUARES ESTIMATION OF

THE MEAN FUNCTION OF A COUNTING PROCESS

BASED ON PANEL COUNTS

X. Joan Hu$^1$, Stephen W. Lagakos$^2$ and Richard A. Lockhart$^1$

$^1$Simon Fraser University and $^2$Harvard School of Public Health

Abstract: 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 Sun and Kalbfleisch (1995), and are closely related to the nonparametric maximum likelihood estimator studied in Wellner and Zhang (2000). 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.

Key words and phrases: Isotonic regression, monotonicity constraint, periodic observations.