The global errors ISE (Integrated Squared Error), MISE (Mean Integrated Squared Error) and the AMISE (Asymptotic Mean Integrated Squared Error) for 1- to 6-dimensional data. Normal mixture densities have closed form expressions for the MISE and AMISE. So in these cases, we can numerically minimise these criteria to find MISE- and AMISE-optimal matrices.
Hamise.mixt(mus, Sigmas, props, samp, Hstart, deriv.order=0)
Hmise.mixt(mus, Sigmas, props, samp, Hstart, deriv.order=0)
Hamise.mixt.diag(mus, Sigmas, props, samp, Hstart, deriv.order=0)
Hmise.mixt.diag(mus, Sigmas, props, samp, Hstart, deriv.order=0)
hamise.mixt(mus, sigmas, props, samp, hstart, deriv.order=0)
hmise.mixt(mus, sigmas, props, samp, hstart, deriv.order=0)
amise.mixt(H, mus, Sigmas, props, samp, h, sigmas, deriv.order=0)
ise.mixt(x, H, mus, Sigmas, props, h, sigmas, deriv.order=0, binned=FALSE,
bgridsize)
mise.mixt(H, mus, Sigmas, props, samp, h, sigmas, deriv.order=0)
(stacked) matrix of mean vectors (>1-d), vector of means (1-d)
(stacked) matrix of variance matrices (>1-d), vector of standard deviations (1-d)
vector of mixing proportions
sample size
initial bandwidth (matrix), used in numerical optimisation
derivative order
matrix of data values
bandwidth (matrix)
flag for binned kernel estimation. Default is FALSE.
vector of binning grid sizes
Unconstrained MISE- or AMISE-optimal bandwidth matrix. ISE, MISE or AMISE value.
ISE is a random variable that depends on the data
x
. MISE and AMISE are non-random and don't
depend on the data. For normal mixture densities, ISE, MISE and AMISE
have exact formulas for all dimensions.
Chacon J.E., Duong, T. & Wand, M.P. (2011). Asymptotics for general multivariate kernel density derivative estimators. Statistica Sinica. 21, 807-840.
# NOT RUN {
x <- rmvnorm.mixt(100)
Hamise.mixt(samp=nrow(x), mus=rep(0,2), Sigmas=var(x), props=1, deriv.order=1)
# }
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