Estimation of spanning tree mean-edge using node sampling

Article type: Research Article

Authors: Shukla, D. | Rajput, Yashwant Singh | Thakur, Narendra Singh

Affiliations: Department of Mathematics and Statistics, Sagar University, Sagar (M. P.) 470003, India. E-mails: diwakarshukla@rediffmail.com, nst_stats@yahoo.co.in

Abstract: Suppose a finite graph containing several vertices, each connected with single or multiple edges. This constitutes a graph population of vertices and edges for example, the population like a tree having a sub-graph in the form of spanning tree. The paper contains mixture of the graph structure and sampling procedure together by virtue of mean-edge estimation of spanning tree using the remaining edges of graph as an auxiliary source of information. A new sampling procedure (node sampling) is derived for this purpose and estimation strategy is proposed to obtain this goal. An optimal sub-class of estimators is obtained. Mathematical conditions for minimum bias and optimum mean squared error are derived and theoretical results are numerically supported with the help of an example of graph population. Almost all the sample estimates of mean-edge length of spanning tree are found within the confidence limits.

Keywords: Graph, tree, spanning tree, vertices (nodes), simple random sampling without replacement (SRSWOR), bias, mean squared error (MSE), optimum choice, confidence interval

DOI: 10.3233/MAS-2009-0105

Journal: Model Assisted Statistics and Applications, vol. 4, no. 1, pp. 23-37, 2009