`R/estimate_mle2.R`

`estimate_mle2.Rd`

Authors argue that the approach proposed in `est.mle1`

is
empirically bias-prone in that the averaging of sample statistics over
all data points is taken to be a harmonic manner.

`est.mle2(X, k1 = 10, k2 = 20)`

- X
an \((n\times p)\) matrix or data frame whose rows are observations.

- k1
minimum neighborhood size, larger than 1.

- k2
maximum neighborhood size, smaller than \(n\).

a named list containing containing

- estdim
estimated intrinsic dimension.

MacKay DJC, Ghahramani Z (2005). “Comments on 'Maximum Likelihood Estimation of Intrinsic Dimension' by E. Levina and P. Bickel (2004).” https://www.inference.org.uk/mackay/dimension/.

```
# \donttest{
## create example data sets with intrinsic dimension 2
X1 = aux.gensamples(dname="swiss")
X2 = aux.gensamples(dname="ribbon")
X3 = aux.gensamples(dname="saddle")
## acquire an estimate for intrinsic dimension
out1 = est.mle2(X1)
out2 = est.mle2(X2)
out3 = est.mle2(X3)
line1 = paste0("* est.mle2 : dimension of 'swiss' data is ",round(out1$estdim,2))
line2 = paste0("* est.mle2 : dimension of 'ribbon' data is ",round(out2$estdim,2))
line3 = paste0("* est.mle2 : dimension of 'saddle' data is ",round(out3$estdim,2))
cat(paste0(line1,"\n",line2,"\n",line3))
#> * est.mle2 : dimension of 'swiss' data is 1.99
#> * est.mle2 : dimension of 'ribbon' data is 2
#> * est.mle2 : dimension of 'saddle' data is 2.19
# }
```