p2: a random effects model with covariates for directed graphs

A random effects model is proposed for the analysis of binary dyadic data that represent a social network or directed graph, using nodal and/or dyadic attributes as covariates. The network structure is reflected by modeling the dependence between the relations to and from the same actor or node. Parameter estimates are proposed that are based on an iterated generalized least-squares procedure. An application is presented to a data set on friendship relations between American lawyers.     

Asymptotic and Bootstrap techniques for testing the expected value of a fuzzy random variable

In this paper we will consider hypothesis-tests for the (fuzzy-valued) mean value of a fuzzy random variable in a population. For this purpose, we will make use of a generalized metric for fuzzy numbers, and we will develop an approach for normal fuzzy random variables, and two different approaches for the case of fuzzy random variables taking on a finite number of different values. A real-life example illustrates the use of the last two approaches. Finally, a comparison between the introduced techniques is developed by means of simulation studies leading to close inferential conclusions.Acknowledgements.The research in this paper has been partially supported by MCYT Grants BFM2002-01057 and BFM2001-3494. Their financial support is gratefully acknowledged. The authors are sincerely grateful to their colleague Gil González-Rodríguez for all his comments and suggestions in connection with this paper; his scientific support has been very valuable. The authors want also thank the referees of the first version of the paper because of their useful hints to improve it.     

On optimal allocations for estimating the surface of a random field

In general, the construction of optimal designs is apparently a difficult task for the approximation of a random field indexed by more than one dimension. Besides the rate of convergence of the minimum achievable error hardly anything is known until now. However, if there is an immanent structure present in the random field, then, taking this structure into account, improved estimates can be obtained. For this situation we present adequate designs which show, at least, a nearly optimal performance. work supported by 313/ARC/VII/93/151 of the DAAD work supported by Ku719/2-1 of the DFG     

Remarks on the strong law of large numbers for a triangular array of associated random variables

A strong law of large numbers for a triangular array of strictly stationary associated random variables is proved. It is used to derive the pointwise strong consistency of kernel type density estimator of the one-dimensional marginal density function of a strictly stationary sequence of associated random variables, and to obtain an improved version of a result by Van Ryzin (1969) on the strong consistency of density estimator for a sequence of independent and identically distributed random variables.     

The distribution function of a statistic for testing the equality of scale parameters in two gamma populations

Summary The exact distribution function of the ratio of two sums of gamma variates is derived in this paper. The result applies to ratios of quadratic forms and to a statistic used for testing the equality of scale parameters in two gamma populations.