Abstract

Abstract

Abstract

Abstract
We address classification of distributional data, where units are described by histogram or interval-valued variables. The proposed approach uses a linear discriminant function where distributions or intervals are represented by quantile functions, under specific assumptions. This discriminant function allows defining a score for each unit, in the form of a quantile function, which is used to classify the units in two a priori groups, using the Mallows distance. There is a diversity of application areas for the proposed linear discriminant method. In this work we classify the airline companies operating in NY airports based on air time and arrival/departure delays, using a full year flights.

Abstract
We compare two interval time series (ITS) by testing whether their underlying distributions are significantly different or not. To perform hypothesis testing, we make use of the discrete wavelet transform (DWT) which decomposes a time series into a set of coefficients over a number of frequency bands or scales. We obtain the DWT of the radius and centre of each of the two ITS at different scales, and perform randomisation tests. In order to use a randomisation test, the observations must be uncorrelated; this condition is more or less satisfied since at each scale, the DWT coefficients are approximately uncorrelated with each other. Our proposed test statistic is the ratio of the determinants of the covariance matrix of radius and centre DWTs of the two ITS, at each scale. This test statistic ensures that the variability between the upper and lower bounds of each ITS is encompassed. Simulation studies conducted to evaluate the performance of the test show reasonably good estimates of size and power under most conditions, and applications to real interval time series reveal the practical usefulness of this test.

Abstract
We present the CRAN R package MAINT.Data for the modelling and analysis of multivariate interval data, i.e., where units are described by variables whose values are intervals of IR, representing intrinsic variability. Parametric inference methodologies based on probabilistic models for interval variables have been developed, where each interval is represented by its midpoint and log-range, for which multivariate Normal and Skew-Normal distributions are assumed. The intrinsic nature of the interval variables leads to special structures of the variance-covariance matrix, which are represented by four different possible configurations. MAINT.Data implements the proposed methodologies in the S4 object system, introducing a specific data class for representing interval data. It includes functions and methods for modelling and analysing interval data, in particular maximum likelihood estimation, statistical tests for the different configurations, (M)ANOVA and Discriminant Analysis. For the Gaussian model, Model-based Clustering, robust estimation, outlier detection and Robust Discriminant Analysis are also available.