Identifying arbitrary transformation between the slopes in functional regression

Colloquium Talk

Title

Identifying arbitrary transformation between the slopes in functional regression

Abstract

In this talk, we study whether the slope functions of two functional regression models in two samples are associated with any arbitrary transformation (barring constant and linear transformation) or not along the vertical axis. In order to address this issue, a statistical testing of the hypothesis problem is formalized, and the test statistic is formed based on the estimated second derivative of the unknown transformation. The asymptotic properties of the test statistics are investigated using some advanced techniques related to the empirical process. Moreover, to implement the test for small sample size data, a Bootstrap algorithm is proposed, and it is shown that the Bootstrap version of the test is as good as the original test for sufficiently large sample size. Furthermore, the utility of the proposed methodology is shown for simulated data sets, and DTI data is analyzed using this methodology.  This is a joint work with Pratim Guha Niyogi (Johns Hopkins University, USA).

Speaker Bio

Subhra Sankar Dhar completed his PhD in Statistics in 2012 from the Indian Statistical Institute, Calcutta. He has extensive academic experience, including a Postdoctoral Research Associate position at the University of Cambridge, England, and faculty roles at Presidency University and IIT Kanpur, India. Additionally, he served as a Visiting Assistant Professor at Michigan State University, USA. His contributions to the field of statistics have been recognized through prestigious awards, including the National Award in Statistics in honor of Prof. C. R. Rao, awarded by the Ministry of Statistics & Programme Implementation, Government of India in 2019. He also received the P K Kelkar Research Fellowship from IIT Kanpur for his excellent professional contributions. In addition to his academic accolades, he is the Principal Modeller from IIT Kanpur in the National Disease Modelling Consortium (NDMC), leading research on typhoid fever, funded by the Bill & Melinda Gates Foundation. His research interests include non-parametric function estimation, measures of association, multivariate quantiles and ranks, data depth, and robust statistical methods.