We discuss nonparametric estimation of the distribution function G(x) of the autoregressive coefficient from a panel of N random-coefficient AR(1) data, each of length n, by the empirical distribution of lag 1 sample correlations of individual AR(1) processes. Consistency and asymptotic normality of the empirical distribution function and a class of kernel density estimators is established unde...

Most statistics students know that the sample correlation coefficient R is used to estimate the population correlation coefficient ρ. If the pair (X, Y) has a bivariate normal distribution, this would not cause any trouble. However, if the marginals are nonnormal, particularly if they have high skewness and kurtosis, the estimated value from a sample may be quite different from the population c...

Current metrics used in summarizing networks, such as degree distribution, average diameter and clustering coefficient, provide a very coarse understanding of their structure. One would like to have finergrained summaries of networks which allow making distinction between structurally different networks. A class of such interesting graph statistics are the Small Subgraph Frequencies. These subg...

In this paper, a new local-world evolving network model including triad formation mechanism is proposed and studied. Analytical expressions for degree distribution and clustering coefficient are derived using continuum theory. It is shown that the degree distribution transfers from exponential to power-law scaling, and the clustering coefficient is tunable with known parameters. Finally, the nu...