Implements Kernel-based Regularized Least Squares (KRLS), a
    machine learning method to fit multidimensional functions y = f(x) for
    regression and classification problems without relying on linearity or
    additivity assumptions. KRLS finds the best fitting function by
    minimizing the squared loss of a Tikhonov regularization problem,
    using Gaussian kernels as radial basis functions. For further details
    see Hainmueller and Hazlett (2014, <doi:10.1093/pan/mpt019>).

Implements several methods for testing the variance component parameter in regression models that contain kernel-based random effects, including a maximum of adjusted scores test. Several kernels are supported, including a profile hidden Markov model mutual information kernel for protein sequence. This package is described in Fong et al. (2015) <DOI:10.1093/biostatistics/kxu056>.

Solves kernel ridge regression, within the the mixed model framework, for the linear, polynomial, Gaussian, Laplacian and ANOVA kernels. The model components (i.e. fixed and random effects) and variance parameters are estimated using the expectation-maximization (EM) algorithm. All the estimated components and parameters, e.g. BLUP of dual variables and BLUP of random predictor effects for the linear kernel (also known as RR-BLUP), are available. The kernel ridge mixed model (KRMM) is described in Jacquin L, Cao T-V and Ahmadi N (2016) A Unified and Comprehensible View of Parametric and Kernel Methods for Genomic Prediction with Application to Rice. Front. Genet. 7:145. <doi:10.3389/fgene.2016.00145>.

Kronecker-invariant tests for high-dimensional separability testing of matrix-variate data, focusing on Gaussian populations as benchmark cases. Tests whether the population covariance matrix is represented as a Kronecker product of row and column covariance matrices. Implements the tests based on the eigenvalues of the sample core whose test statistics are invariant to the separable component of the population covariance matrix, referred to as Kronecker-invariance. Tests constructed using the largest eigenvalue and the separable expansion of the sample core and applying the extended likelihood ratio test for sphericity testing to the sample core. For details, see Sung and Hoff (2025) <doi:10.48550/arXiv.2506.17463>.