Nearest neighbour analysis of random distributions on a sphere

Convergence of random k-nearest-neighbour imputation

Random k-nearest-neighbour (RKNN) imputation is an established algorithm for filling in missing values in data sets. Assume that data are missing in a random way, so that missingness is independent of unobserved values (MAR), and assume there is a minimum positive probability of a response vector being complete. Then RKNN, with k equal to the square root of the sample size, asymptotically produ...

CONNECTIVITY OF RANDOM k-NEAREST-NEIGHBOUR GRAPHS

LetP be a Poisson process of intensity one in a squareSn of arean. We construct a random geometric graph Gn,k by joining each point of P to its k ≡ k(n) nearest neighbours. Recently, Xue and Kumar proved that if k ≤ 0.074 log n then the probability that Gn,k is connected tends to 0 as n → ∞ while, if k ≥ 5.1774 log n, then the probability that Gn,k is connected tends to 1 as n → ∞. They conject...

On the Connectivity of Random k-th Nearest Neighbour Graphs

On the layered nearest neighbour estimate, the bagged nearest neighbour estimate and the random forest method in regression and classification

Let X1, . . . ,Xn be identically distributed random vectors in R d, independently drawn according to some probability density. An observation Xi is said to be a layered nearest neighbour (LNN) of a point x if the hyperrectangle defined by x and Xi contains no other data points. We first establish consistency results on Ln(x), the number ∗The second author’s research was sponsored by NSERC Grant...

Title Nearest Neighbour Contingency Table Analysis

March 19, 2012 Type Package Title Nearest Neighbour Contingency Table Analysis Version 0.0-3 Date 2012-03-19 Author Marcelino de la Cruz Rot and Philip M. Dixon Maintainer Marcelino de la Cruz Rot Depends splancs, spatstat Description Function to test spatial segregation and association based in contingency table analysis of nearest neighbour counts following Dixon (...