# Statistics

## 1105 Submissions

[2] **viXra:1105.0038 [pdf]**
*submitted on 25 May 2011*

### The Numerical Generalised Least-Squares Estimator of an Unknown Constant Mean of Randon Field

**Authors:** T Suslo

**Comments:** 9 pages.

We constraint on computer the best linear unbiased generalized statistics of
random field for the best linear unbiased generalized statistics of
an unknown constant mean of random field and derive the numerical
generalized least-squares estimator of an unknown constant mean of
random field. We derive the third constraint of spatial ststistics and show
that the classic generalized least-squares estimator of
an unknown constant mean of the field is only an asymptotic disjunction of
the numerical one.

**Category:** Statistics

[1] **viXra:1105.0026 [pdf]**
*submitted on 16 May 2011*

### Asymptotic Moments of Near Neighbor Distances for the Gaussian Distribution

**Authors:** Elia Liitiäinen

**Comments:** 37 pages, Submitted to a journal

We study the moments E[d_{1,k}^{α}]
of the k-th nearest neighbor distance
for independent identically distributed points in R^{n}. In the earlier
literature, the case α > n has been analyzed by assuming a bounded support
for the underlying density. The boundedness assumption is removed by
assuming the multivariate Gaussian distribution. In this case, the nearest
neighbor distances show very different behavior in comparison to earlier
results. In the unbounded case, it is shown that E[d_{1,k}^{α}] is asymptotically
proportional to M^{-1} log^{n-1-α/2}M instead of M^{-α/n} as in the previous
literature.

**Category:** Statistics