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
xmlui.dri2xhtml.METS-1.0.item-contributor-funder:
Ministerio de Economía y Competitividad (España)
Sponsor:
UK Medical Research Council, Grant/Award Numbers: MR/M020894/1, MC_UU_12013/7 MC_UU_12013/5; Wellcome Trust, Grant/Award Numbers:WT087997MA and 102215/2/13/2; Spanish Ministry of Economy and Competitiveness, Grant/Award number: MTM2014‐52184; National Institute forHealth Research (NIHR), Grant/AwardNumber: NF‐SI‐0611‐10196; University ofBristol; British Heart Foundation, Grant/Award Number: SP/07/008/24066; USNIH, Grant/Award Number: R01 DK077659
Project:
Gobierno de España. MTM2014-52184-P
Keywords:
ALSPAC
,
Derivative estimation
,
Functional data analysis
,
Longitudinal data analysis
,
Penalized splines
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 DarIn 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.[+][-]