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

Area of Science:

• Statistics
• Biostatistics
• Survival Analysis

Background:

• Counting processes are fundamental in modeling event occurrences over time.
• Panel count data, arising from periodic observations, presents unique estimation challenges.
• Existing methods may lack efficiency in non-Poisson counting processes.

Purpose of the Study:

• To develop novel nonparametric estimators for the mean function of counting processes with panel count data.
• To ensure estimators satisfy monotonicity constraints, reflecting the nature of event counts.
• To provide computationally feasible procedures for implementing these new estimators.

Main Methods:

• Generalized sums of squares minimization subject to monotonicity constraints.
• Development of estimators related to existing methods like Sun and Kalbfleisch (1995) and Wellner and Zhang (2000).
• Exploration of various weight functions to tailor estimator performance.

Main Results:

• Theoretical consistency of the proposed nonparametric estimators is established.
• Demonstration that specific weight functions yield known estimators.
• Identification of alternative weight functions offering superior efficiency in non-Poisson settings.
• Simulation studies confirm the finite-sample performance of the new estimators.

Conclusions:

• The proposed generalized sum of squares approach provides robust nonparametric estimation for counting processes with panel count data.
• These estimators offer a valuable alternative, particularly when the underlying process deviates from Poisson assumptions.
• The study contributes practical and theoretically sound methods for analyzing complex event data.