Estimating historic movement of a climatological variable from a pair of misaligned data sets

TL;DR

This paper proposes a registration-based method for estimating the mean of paleoclimatic data sets, demonstrating that proper alignment improves estimation accuracy despite registration errors, with theoretical and empirical validation.

Contribution

It introduces a registration approach for paleoclimatic data, showing its theoretical consistency and practical benefits over traditional methods that ignore misalignment.

Findings

Registration improves mean estimation accuracy.

Consistent time transformation estimators ensure reliable results.

Simulation and real data analysis confirm the method's effectiveness.

Abstract

We consider in this paper the problem of estimating the mean function from a pair of paleoclimatic functional data sets, after one of them has been registered with the other. We show theoretically that registering one data set with respect to the other is the right way to formulate this problem, which is in contrast with estimation of the mean function in a "neutral" time scale that is preferred in the analysis of multiple sets of longitudinal growth data. Once this registration is done, the Nadaraya-Watson estimator of the mean function may be computed from the pooled data. We show that, if a consistent estimator of the time transformation is used for this registration, the above estimator of the mean function would be consistent under a few additional conditions. We study the potential change in asymptotic mean squared error of the estimator that may be possible because of the contribution of the time-transformed data set. After demonstrating through simulation that the additional data can lead to improved estimation in spite of estimation error in registration, we estimate the mean function of three pairs of paleoclimatic data sets. The analysis reveals some interesting aspects of the data sets and the estimation problem.