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This paper introduces a novel density estimator supported on $d$-dimensionalhalf-spaces. It stands out as the first asymmetric kernel density estimator forhalf-spaces in the literature. Using the multivariate inverse Gaussian (MIG)density from Minami (2003) as the kernel and incorporating locally adaptiveparameters, the estimator achieves desirable boundary properties. To analyzeits mean integrated squared error (MISE) and asymptotic normality, a locallimit theorem and probability metric bounds are established between the MIG andthe corresponding multivariate Gaussian distribution with the same mean vectorand covariance matrix, which may also be of independent interest. Additionally,a new algorithm for generating MIG random vectors is developed, proving to befaster and more accurate than Minami's algorithm based on a Brownianfirst-hitting location representation. This algorithm is then used to discussand compare optimal MISE and likelihood cross-validation bandwidths for theestimator in a simulation study under various target distributions. As anapplication, the MIG asymmetric kernel is used to smooth the posteriordistribution of a generalized Pareto model fitted to large electromagneticstorms.

Normal approximations for the multivariate inverse Gaussian distribution and asymmetric kernel smoothing on $d$-dimensional half-spaces