Publication:
Derivative estimation for longitudinal data analysis

Loading...
Thumbnail Image
Identifiers
Publication date
2018-08-30
Defense date
Advisors
Tutors
Journal Title
Journal ISSN
Volume Title
Publisher
John Wiley & Sons
Impact
Google Scholar
Export
Research Projects
Organizational Units
Journal Issue
Abstract
In a previous paper we derived equivalence relations for pseudo-Wronskian determinants of Hermite polynomials. In this paper we obtain the analogous result for Laguerre and Jacobi polynomials. The equivalence formulas are richer in this case since rational Darboux transformations can be defined for four families of seed functions, as opposed to only two families in the Hermite case. The pseudo-Wronskian determinants of Laguerre and Jacobi type will thus depend on two Maya diagrams, while Hermite pseudo-Wronskians depend on just one Maya diagram. We show that these equivalence relations can be interpreted as the general transcription of shape invariance and specific discrete symmetries acting on the parameters of the isotonic oscillator and Darboux-Poschl-Teller potential.
Description
Keywords
ALSPAC, Derivative estimation, Functional data analysis, Longitudinal data analysis, Penalized splines
Bibliographic citation
Simpkin, AJ, Durban, M, Lawlor, DA, et al. Derivative estimation for longitudinal data analysis: Examining features of blood pressure measured repeatedly during pregnancy. Statistics in Medicine. 2018; 37: 2836– 2854