Joint models for grid point and response processes in longitudinal and functional data

TL;DR

This paper introduces a covariation model for jointly analyzing grid point locations and response processes in functional data, revealing their interdependence through maximum likelihood estimation and application to auction data.

Contribution

It develops a novel joint modeling approach treating data as a marked point process, enabling inference on the relationship between observation points and responses.

Findings

Strong correlation between bidding patterns and price trajectories

Model effectively estimates interdependence in functional data

Simulation studies validate estimator performance

Abstract

The distribution of the grid points at which a response function is observed in longitudinal or functional data applications is often informative and not independent of the response process. In this paper we introduce a covariation model to estimate and make inferences about this interrelation, by treating the data as replicated realizations of a marked point process. We derive maximum likelihood estimators, the asymptotic distribution of the estimators, and study the estimators' behavior by simulation. We apply the model to an online auction data set and show that there is a strong correlation between bidding patterns and price trajectories.