Description Usage Arguments Details Examples

Computes the MSE of the Local Non-Uniformity Correct (LNC) KSG estimator for a given value of the tuning parameter `alpha`

, dimension, neighborhood order, and sample size.

1 2 | ```
estimate_mse(k = 5, alpha = 0, d = 2, rho = 0, N = 1000,
M = 100, cluster = NULL)
``` |

`k` |
Neighborhood order. |

`alpha` |
Non-uniformity threshold (see details). |

`d` |
Dimension. |

`rho` |
Reference correlation (see details). |

`N` |
Sample size. |

`M` |
Number of replications. |

`cluster` |
A |

The parameter `alpha`

controls the threshold for the application of the non-uniformity correction to a particular point's neighborhood. Roughly, `alpha`

is the ratio of the PCA aligned neighborhood volume to the rectangular aligned neighborhood volume below which indicates non-uniformity and the correction is applied.

If `alpha < 0`

then a log scale is assumed; otherwise [0,1] scale is used. `alpha > 1`

are unacceptable values. A value of `alpha = 0`

forces no correction and LNC reverts to the KSG estimator.

The reference distribution that is assumed is a mean-zero multivariate normal distribution with a compound-symmetric covariance. The covariance matrix has a single correlation parameter supplied by `rho`

.

1 | ```
estimate_mse(N = 100,M = 2)
``` |

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