Provides a weighting approach that employs kernels to make one group have a similar distribution to another group on covariates. This method matches not only means or marginal distributions but also higher-order transformations implied by the choice of kernel. 'kbal' is applicable to both treatment effect estimation and survey reweighting problems. Based on Hazlett, C. (2020) "Kernel Balancing: A flexible non-parametric weighting procedure for estimating causal effects." Statistica Sinica. <https://www.researchgate.net/publication/299013953_Kernel_Balancing_A_flexible_non-parametric_weighting_procedure_for_estimating_causal_effects>.

Computes Khattree-Bahuguna's univariate and multivariate skewness, principal-component-based Khattree-Bahuguna's multivariate skewness. It also provides several measures of univariate or multivariate skewnesses including, Pearson’s coefficient of skewness, Bowley’s univariate skewness and Mardia's multivariate skewness. See Khattree, R. and Bahuguna, M. (2019) <doi: 10.1007/s41060-018-0106-1>.

Implementation of the KCMeans regression estimator studied by 
    Wiemann (2023) <arXiv:2311.17021> for expectation function estimation conditional on 
    categorical variables. Computation leverages the unconditional KMeans 
    implementation in one dimension using dynamic programming algorithm of
    Wang and Song (2011) <doi:10.32614/RJ-2011-015>, allowing for global solutions in time polynomial in 
    the number of observed categories.

Implements approaches of non-parametric smooth test to 
            compare simultaneously K(K>1) copulas and non-parametric clustering 
            of multivariate populations with arbitrary sizes. 
            See Yves I. Ngounou Bakam and Denys Pommeret (2022) <arXiv:2112.05623> and
            Yves I. Ngounou Bakam and Denys Pommeret (2022) <arXiv:2211.06338>.

The running statistics of interest is first extracted using a time window which is slid across the time series, and in each window, the running statistics value is computed. KCP (Kernel Change Point) detection proposed by Arlot et al. (2012) <arXiv:1202.3878> is then implemented to flag the change points on the running statistics (Cabrieto et al., 2018, <doi:10.1016/j.ins.2018.03.010>). Change points are located by minimizing a variance criterion based on the pairwise similarities between running statistics which are computed via the Gaussian kernel. KCP can locate change points for a given k number of change points. To determine the optimal k, the KCP permutation test is first carried out by comparing the variance of the running statistics extracted from the original data to that of permuted data. If this test is significant, then there is sufficient evidence for at least one change point in the data. Model selection is then used to determine the optimal k>0.