Modal clustering of matrix-variate data.

The nonparametric formulation of density-based clustering, known as modal clustering, draws a correspondence between groups and the attraction domains of the modes of the density function underlying the data. Its probabilistic foundation allows for a natural, yet not trivial, generalization of the approach to the matrix-valued setting, increasingly widespread, for example, in longitudinal and multivariate spatio-temporal studies. In this work we introduce nonparametric estimators of matrix-variate distributions based on kernel methods, and analyze their asymptotic properties. Additionally, we propose a generalization of the mean-shift procedure for the identification of the modes of the estimated density. Given the intrinsic high dimensionality of matrix-variate data, we discuss some locally adaptive solutions to handle the problem. We test the procedure via extensive simulations, also with respect to some competitors, and illustrate its performance through two high-dimensional real data applications.

Co-clustering of Time-Dependent Data via the Shape Invariant Model.

Multivariate time-dependent data, where multiple features are observed over time for a set of individuals, are increasingly widespread in many application domains. To model these data, we need to account for relations among both time instants and variables and, at the same time, for subject heterogeneity. We propose a new co-clustering methodology for grouping individuals and variables simultaneously, designed to handle both functional and longitudinal data. Our approach borrows some concepts from the curve registration framework by embedding the shape invariant model in the latent block model, estimated via a suitable modification of the SEM-Gibbs algorithm. The resulting procedure allows for several user-defined specifications of the notion of cluster that can be chosen on substantive grounds and provides parsimonious summaries of complex time-dependent data by partitioning data matrices into homogeneous blocks. Along with the explicit modelling of time evolution, these aspects allow for an easy interpretation of the clusters, from which also low-dimensional settings may benefit.

Comment on "Wang et al. (2005), Robust estimating functions and bias correction for longitudinal data analysis".

This note provides a discussion on the manuscript by Wang et al. (2005) who aim to robustify inference for longitudinal data analysis by replacing the ordinary generalized estimating function with an influence-bounded, possibly biased, version. To adjust for the bias of the ensuing robust estimator, the authors provide its analytic approximation by means of asymptotic expansions, and estimate it by plugging-in a nonrobust estimate of the parameter of interest. In this letter, we argue that the proposed bias-corrected estimator is, in fact, nonrobust.