Routines for model-based functional cluster analysis for functional data with optional covariates. The idea is to cluster functional subjects (often called functional objects) into homogenous groups by using spline smoothers (for functional data) together with scalar covariates. The spline coefficients and the covariates are modelled as a multivariate Gaussian mixture model, where the number of mixtures corresponds to the number of clusters. The parameters of the model are estimated by maximizing the observed mixture likelihood via an EM algorithm (Arnqvist and Sjöstedt de Luna, 2019) <doi:10.48550/arXiv.1904.10265>. The clustering method is used to analyze annual lake sediment from lake Kassjön (Northern Sweden) which cover more than 6400 years and can be seen as historical records of weather and climate.

Performs analysis of variance testing procedures for univariate and multivariate functional data (Cuesta-Albertos and Febrero-Bande (2010) <doi:10.1007/s11749-010-0185-3>, Gorecki and Smaga (2015) <doi:10.1007/s00180-015-0555-0>, Gorecki and Smaga (2017) <doi:10.1080/02664763.2016.1247791>, Zhang et al. (2018) <doi:10.1016/j.csda.2018.05.004>).

A collection of functions for outlier detection in functional data analysis. 
  Methods implemented include directional outlyingness by 
  Dai and Genton (2019) <doi:10.1016/j.csda.2018.03.017>,
  MS-plot by Dai and Genton (2018) <doi:10.1080/10618600.2018.1473781>,
  total variation depth and modified shape similarity index by 
  Huang and Sun (2019) <doi:10.1080/00401706.2019.1574241>, and sequential transformations by
  Dai et al. (2020) <doi:10.1016/j.csda.2020.106960 among others. Additional outlier detection
  tools and depths for functional data like functional boxplot, (modified) band depth etc.,
  are also available.

A versatile package that provides implementation of various
    methods of Functional Data Analysis (FDA) and Empirical Dynamics. The core of this
    package is Functional Principal Component Analysis (FPCA), a key technique for
    functional data analysis, for sparsely or densely sampled random trajectories
    and time courses, via the Principal Analysis by Conditional Estimation
    (PACE) algorithm. This core algorithm yields covariance and mean functions,
    eigenfunctions and principal component (scores), for both functional data and
    derivatives, for both dense (functional) and sparse (longitudinal) sampling designs.
    For sparse designs, it provides fitted continuous trajectories with confidence bands,
    even for subjects with very few longitudinal observations. PACE is a viable and
    flexible alternative to random effects modeling of longitudinal data. There is also a
    Matlab version (PACE) that contains some methods not available on fdapace and vice
    versa. Updates to fdapace were supported by grants from NIH Echo and NSF DMS-1712864 and DMS-2014626. 
    Please cite our package if you use it (You may run the command citation("fdapace") to get the citation format and bibtex entry).
    References: Wang, J.L., Chiou, J., Müller, H.G. (2016) <doi:10.1146/annurev-statistics-041715-033624>; Chen, K., Zhang, X., Petersen, A., Müller, H.G. (2017) <doi:10.1007/s12561-015-9137-5>.