Nonparametric estimation of interaction functions for two-type pairwise interaction point processes

Nonparametric Estimation of Interaction Functions of Pairwise Interaction Point Processes

The new problem of nonparametric estimation of the interaction function of pairwise interaction point processes is addressed. We rst generalize some limit theorems of Saunders and Funk. Then we propose a very simple nonparametric estimation method based on the generalization. Several examples are shown to illustrate its eecacy.

Wavelets for Nonparametric Stochastic Regression with Pairwise Negative Quadrant Dependent Random Variables

We propose a wavelet based stochastic regression function estimator for the estimation of the regression function for a sequence of pairwise negative quadrant dependent random variables with a common one-dimensional probability density function. Some asymptotic properties of the proposed estimator are investigated. It is found that the estimators have similar properties to their counterparts st...

Parametric estimation of pairwise Gibbs point processes with infinite range interaction

On a Theory of Nonparametric Pairwise Similarity for Clustering: Connecting Clustering to Classification

Pairwise clustering methods partition the data space into clusters by the pairwise similarity between data points. The success of pairwise clustering largely depends on the pairwise similarity function defined over the data points, where kernel similarity is broadly used. In this paper, we present a novel pairwise clustering framework by bridging the gap between clustering and multi-class class...

Moment Inequalities for Supremum of Empirical Processes of‎ ‎U-Statistic Structure and Application to Density Estimation

We derive moment inequalities for the supremum of empirical processes of U-Statistic structure and give application to kernel type density  estimation ‎and estimation of the distribution function for functions of observations.