TY - JOUR

T1 - Application of the empirical characteristic function to compare and estimate densities by pooling information.

AU - Ferré, L.

AU - Whittaker, Joseph

PY - 2004/5

Y1 - 2004/5

N2 - Independent measurements are taken from distinct populations which may differ in mean, variance and in shape, for instance in the number of modes and the heaviness of the tails. Our goal is to characterize differences between these different populations. To avoid pre-judging the nature of the heterogeneity, for instance by assuming a parametric form, and to reduce the loss of information by calculating summary statistics, the observations are transformed to the empirical characteristic function (ECF). An eigen decomposition is applied to the ECFs to represent the populations as points in a low dimensional space and the choice of optimal dimension is made by minimising a mean square error. Interpretation of these plots is naturally provided by the corresponding density estimate obtained by inverting the ECF projected on the reduced dimension space. Some simulated examples indicate the promise of the technique and an application to the growth of Mirabilis plants is given.

AB - Independent measurements are taken from distinct populations which may differ in mean, variance and in shape, for instance in the number of modes and the heaviness of the tails. Our goal is to characterize differences between these different populations. To avoid pre-judging the nature of the heterogeneity, for instance by assuming a parametric form, and to reduce the loss of information by calculating summary statistics, the observations are transformed to the empirical characteristic function (ECF). An eigen decomposition is applied to the ECFs to represent the populations as points in a low dimensional space and the choice of optimal dimension is made by minimising a mean square error. Interpretation of these plots is naturally provided by the corresponding density estimate obtained by inverting the ECF projected on the reduced dimension space. Some simulated examples indicate the promise of the technique and an application to the growth of Mirabilis plants is given.

KW - complex principal component analysis - empirical characteristic - function - exploratory data analysis - Fourier inversion - growth curve - analysis - kernel density estimation - mean square error - mixture distribution

U2 - 10.1007/BF02892055

DO - 10.1007/BF02892055

M3 - Journal article

VL - 19

SP - 169

EP - 193

JO - Computational Statistics

JF - Computational Statistics

SN - 0943-4062

IS - 2

ER -