  This paper introduces the sparse functional boxplot and the intensity sparse
functional boxplot as practical exploratory tools that make visualization
possible for both complete and sparse functional data. These visualization
tools can be used either in the univariate or multivariate functional setting.
The sparse functional boxplot, which is based on the functional boxplot,
depicts sparseness characteristics in the envelope of the 50\% central region,
the median curve, and the outliers. The proportion of missingness at each time
index within the central region is colored in gray. The intensity sparse
functional boxplot displays the relative intensity of sparse points in the
central region, revealing where data are more or less sparse. The two-stage
functional boxplot, a derivation from the functional boxplot to better detect
outliers, is also extended to its sparse form. Several depth proposals for
sparse multivariate functional data are evaluated and outlier detection is
tested in simulations under various data settings and sparseness scenarios. The
practical applications of the sparse functional boxplot and intensity sparse
functional boxplot are illustrated with two public health datasets.
