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F0(x) is the multivariate normal distribution function Nd(μ, Σ) with mean μ and covariance matrix Σ whose derivative with respect to x is the multivariate probability density function f0(x)= (2π)-d/2 |Σ|½ exp{-½(x-μ)T Σ-1 (x-μ)}.
According to Henze & Wagner (1997) the test statistic in BHEP has a number of favourable characteristics: . it is affine invariant . it is consistent
The test depends on a smoothing parameter h that can be chosen in various ways: Henze & Wagner (1997) recommend h = 1.41, while Tenreiro (2009) recommends hs = 0.448 + 0.026 cd for short tailed alternatives and " " hl = 0.928 + 0.049 cd for long tailed alternatives.
© David Weenink 2010-11-24