L2OptW {IndepTest} | R Documentation |
L2OptW
Description
Calculates a weight vector to be used for the weighted Kozachenko–Leonenko estimator. The weight vector has minimum L_2
norm subject to the linear and sum-to-one constraints of (2) in Berrett, Samworth and Yuan (2018).
Usage
L2OptW(k, d)
Arguments
k |
The tuning parameter that gives the number of neighbours that will be considered by the weighted Kozachenko–Leonenko estimator. |
d |
The dimension of the data. |
Value
The weight vector that is the solution of the optimisation problem.
References
Berrett, T. B., Samworth, R. J. and Yuan, M. (2018). “Efficient multivariate entropy estimation via k-nearest neighbour distances.” Annals of Statistics, to appear.
Examples
# When d < 4 there are no linear constraints and the returned vector is (0,0,...,0,1).
L2OptW(100,3)
w=L2OptW(100,4)
plot(w,type="l")
w=L2OptW(100,8);
# For each multiple of 4 that d increases an extra constraint is added.
plot(w,type="l")
w=L2OptW(100,12)
plot(w, type="l") # This can be seen in the shape of the plot
[Package IndepTest version 0.2.0 Index]