# Ben Barnard

#### 4 packages on CRAN

Testing functions for Covariance Matrices. These tests include high-dimension homogeneity of covariance matrix testing described by Schott (2007) <doi:10.1016/j.csda.2007.03.004> and high-dimensional one-sample tests of covariance matrix structure described by Fisher, et al. (2010) <doi:10.1016/j.jmva.2010.07.004>. Covariance matrix tests use C++ to speed performance and allow larger data sets.

Provides likelihood functions as defined by Fisher (1922) <doi:10.1098/rsta.1922.0009> and a function that creates likelihood functions from density functions. The functions are meant to aid in education of likelihood based methods.

An expansion of R's 'stats' random wishart matrix generation. This package allows the user to generate singular, Uhlig and Harald (1994) <doi:10.1214/aos/1176325375>, and pseudo wishart, Diaz-Garcia, et al.(1997) <doi:10.1006/jmva.1997.1689>, matrices. In addition the user can generate wishart matrices with fractional degrees of freedom, Adhikari (2008) <doi:10.1061/(ASCE)0733-9399(2008)134:12(1029)>, commonly used in volatility modeling. Users can also use this package to create random covariance matrices.

Use multi-state splitting to apply Adaptive-Dynamic PCA (ADPCA) to data generated from a continuous-time multivariate industrial or natural process. Employ PCA-based dimension reduction to extract linear combinations of relevant features, reducing computational burdens. For a description of ADPCA, see <doi:10.1007/s00477-016-1246-2>, the 2016 paper from Kazor et al. The multi-state application of ADPCA is from a manuscript under current revision entitled "Multi-State Multivariate Statistical Process Control" by Odom, Newhart, Cath, and Hering, and is expected to appear in Q1 of 2018.