Description Usage Arguments Value References Examples

Calculates the (weighted) Kozachenko–Leonenko entropy estimator studied in Berrett, Samworth and Yuan (2018), which is based on the *k*-nearest neighbour distances of the sample.

1 |

`x` |
The |

`k` |
The tuning parameter that gives the maximum number of neighbours that will be considered by the estimator. |

`weights` |
Specifies whether a weighted or unweighted estimator is used. If a weighted estimator is to be used then the default ( |

`stderror` |
Specifies whether an estimate of the standard error of the weighted estimate is calculated. The calculation is done using an unweighted version of the variance estimator described on page 7 of Berrett, Samworth and Yuan (2018). |

The first element of the list is the unweighted estimator for the value of 1 up to the user-specified *k*. The second element of the list is the weighted estimator, obtained by taking the inner product between the first element of the list and the weight vector. If `stderror=TRUE`

the third element of the list is an estimate of the standard error of the weighted estimate.

BSY2017IndepTest

1 2 3 4 5 | ```
n=1000; x=rnorm(n); KLentropy(x,30,stderror=TRUE) # The true value is 0.5*log(2*pi*exp(1)) = 1.42.
n=5000; x=matrix(rnorm(4*n),ncol=4) # The true value is 2*log(2*pi*exp(1)) = 5.68
KLentropy(x,30,weights=FALSE) # Unweighted estimator
KLentropy(x,30,weights=TRUE) # Weights chosen by L2OptW
w=runif(30); w=w/sum(w); KLentropy(x,30,weights=w) # User-specified weights
``` |

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