  This paper introduces a novel density estimator supported on $d$-dimensional
half-spaces. It stands out as the first asymmetric kernel smoother for
half-spaces in the literature. Using the multivariate inverse Gaussian (MIG)
density from Minami (2003) as the kernel and incorporating locally adaptive
parameters, the estimator achieves desirable boundary properties. To analyze
its mean integrated squared error (MISE) and asymptotic normality, a local
limit theorem and probability metric bounds are established between the MIG and
the corresponding multivariate Gaussian distribution with the same mean vector
and covariance matrix, which may also be of independent interest. Additionally,
a new algorithm for generating MIG random vectors is developed, proving to be
faster and more accurate than Minami's algorithm based on a Brownian hitting
location representation. This algorithm is then used to discuss and compare
optimal MISE and likelihood cross-validation bandwidths for the estimator in a
simulation study under various target distributions. As an illustration, the
MIG asymmetric kernel is used to smooth the posterior distribution of a
generalized Pareto model fitted to large electromagnetic storms.
