The eigenvalues of observed symmetric matrices are often of intense scientific interest. This package offers single sample tests for the eigenvalues of the population mean or the eigenvalue-multiplicity of the population mean. For k-samples, this package offers tests for equal eigenvalues between samples. Included is support for matrices with constraints common to geophysical tensors (constant trace, sum of squared eigenvalues, or both) and eigenvectors are usually considered nuisance parameters. Pivotal bootstrap methods enable these tests to have good performance for small samples (n=15 for 3x3 matrices). These methods were developed and studied by Hingee, Scealy and Wood (2026, "Nonparametric bootstrap inference for the eigenvalues of geophysical tensors", accepted by the Journal of American Statistical Association). Also available is a 2-sample test using a Gaussian orthogonal ensemble approximation and an eigenvalue-multiplicity test that assumes orthogonally-invariant covariance.

Interface to 'TensorFlow Probability', a 'Python' library built on 'TensorFlow'
    that makes it easy to combine probabilistic models and deep learning on modern hardware ('TPU', 'GPU').
    'TensorFlow Probability' includes a wide selection of probability distributions and bijectors, probabilistic layers,
    variational inference, Markov chain Monte Carlo, and optimizers such as Nelder-Mead, BFGS, and SGLD.

A kernel of functions for programming 
	time series methods in a way that is relatively independently of the 
	representation of time. Also provides plotting, time windowing, 
	and some
	other utility functions which are specifically intended for time series.
	See the Guide distributed as a vignette, or ?tframe.Intro for more
	details. (User utilities are in package tfplot.)

Provide functions to estimate the coefficients in high-dimensional linear regressions via a tuning-free and robust approach. The method was published in Wang, L., Peng, B., Bradic, J., Li, R. and Wu, Y. (2020), "A Tuning-free Robust and Efficient Approach to High-dimensional Regression", Journal of the American Statistical Association, 115:532, 1700-1714(JASA’s discussion paper), <doi:10.1080/01621459.2020.1840989>. See also Wang, L., Peng, B., Bradic, J., Li, R. and Wu, Y. (2020), "Rejoinder to “A tuning-free robust and efficient approach to high-dimensional regression". Journal of the American Statistical Association, 115, 1726-1729, <doi:10.1080/01621459.2020.1843865>; Peng, B. and Wang, L. (2015), "An Iterative Coordinate Descent Algorithm for High-Dimensional Nonconvex Penalized Quantile Regression", Journal of Computational and Graphical Statistics, 24:3, 676-694, <doi:10.1080/10618600.2014.913516>; Clémençon, S., Colin, I., and Bellet, A. (2016), "Scaling-up empirical risk minimization: optimization of incomplete u-statistics", The Journal of Machine Learning Research, 17(1):2682–2717; Fan, J. and Li, R. (2001), "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties", Journal of the American Statistical Association, 96:456, 1348-1360, <doi:10.1198/016214501753382273>.