Premium
Tolerance bands for functional data
Author(s) -
Rathnayake Lasitha N.,
Choudhary Pankaj K.
Publication year - 2016
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.12434
Subject(s) - pointwise , bootstrapping (finance) , range (aeronautics) , principal component analysis , computer science , inference , univariate , functional principal component analysis , population , functional data analysis , algorithm , mathematics , data mining , artificial intelligence , machine learning , econometrics , multivariate statistics , mathematical analysis , materials science , demography , sociology , composite material
Summary Often the object of inference in biomedical applications is a range that brackets a given fraction of individual observations in a population. A classical estimate of this range for univariate measurements is a “tolerance interval.” This article develops its natural extension for functional measurements, a “tolerance band,” and proposes a methodology for constructing its pointwise and simultaneous versions that incorporates both sparse and dense functional data. Assuming that the measurements are observed with noise, the methodology uses functional principal component analysis in a mixed model framework to represent the measurements and employs bootstrapping to approximate the tolerance factors needed for the bands. The proposed bands also account for uncertainty in the principal components decomposition. Simulations show that the methodology has, generally, acceptable performance unless the data are quite sparse and unbalanced, in which case the bands may be somewhat liberal. The methodology is illustrated using two real datasets, a sparse dataset involving CD4 cell counts and a dense dataset involving core body temperatures.