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A Non‐parametric Conditional Bivariate Reference Region with an Application to Height/Weight Measurements on Normal Girls
Author(s) -
Petersen Jorgen Holm
Publication year - 2009
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.200800146
Subject(s) - bivariate analysis , mathematics , statistics , estimator , parametric statistics , bivariate data , multivariate normal distribution , parametric equation , conditional probability distribution , joint probability distribution , growth curve (statistics) , normal distribution , univariate , econometrics , multivariate statistics , geometry
Abstract A conceptually simple two‐dimensional conditional reference curve is described. The curve gives a decision basis for determining whether a bivariate response from an individual is “normal” or “abnormal” when taking into account that a third (conditioning) variable may influence the bivariate response. The reference curve is not only characterized analytically but also by geometric properties that are easily communicated to medical doctors – the users of such curves. The reference curve estimator is completely non‐parametric, so no distributional assumptions are needed about the two‐dimensional response. An example that will serve to motivate and illustrate the reference is the study of the height/weight distribution of 7–8‐year‐old Danish school girls born in 1930, 1950, or 1970.