arXiv subjects

Dibyendu Bhaumik

Publications and source records attributed to Dibyendu Bhaumik.

3 recordsLinked to original sources

arXiv2017

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

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.

stat.ME↗

arXiv2017

Feature Sensitive Curve Registration by Kernel Matching

In this paper, we argue that the problem of registering two sets of functional data, where the underlying mean function has sharp features, is not properly addressed by methods designed to align a bunch of growth curves data. We provide a new method, which is able to pool local information without smoothing and to match sharp landmarks without manual identification. This method, which we refer to as kernel-matched registration, is based on maximizing a kernel-based measure of alignment. We prove that the proposed method is consistent under fairly general conditions. Simulation results show superiority of the performance of the proposed method over two existing methods. The proposed method is illustrated through the analysis of three sets of paleoclimatic data.

stat.ME↗

arXiv2016

Feature Sensitive and Automated Curve Registration

Given two sets of functional data having a common underlying mean function but different degrees of distortion in time measurements, we provide a method of estimating the time transformation necessary to align (or `register') them. We prove that the proposed method is consistent under fairly general conditions. Simulation results show superiority of the performance of the proposed method over two existing methods. The proposed method is illustrated through the analysis of three paleoclimatic data sets.

stat.ME↗