M. Ortego, J. J. Egozcue, J. Graffelman
A multinomial sampling scheme is considered. The proportions of counts in each category are expressed in coordinates through a log-ratio approach. The isometric log-ratio transformation (ilr) has been used. The asymptotic normality of these coordinates is assessed. The normal distribution mean and covariance parameters are expressed as functions of the multinomial probabilities. The development is based on the known mean and variance of a multinomial variable and its asymptotic normal distribution. Following a previous study for trinomial variables (Graffelman, 2011), the delta-method is applied to the maximum likelihood estimators of frequencies in order to provide the asymptotic normal distribution of the isometric log-ratio coordinates. As a consequence, proportions from multinomial counts are asymptotically normal on the simplex. The normal distribution parameters (center and variability) depend only on the multinomial parameters. Two examples are presented.
Palabras clave / Keywords: compositional data, isometric log-ratio transformation
Programado
Sesión GT02-3: Análisis Multivariante y Clasificación (AMyC-3). Organizadora: Eva Boj del Val
29 de mayo de 2018 15:20
Sala 5
