Nonparametric Estimation of Interaction Functions of Pairwise Interaction Point Processes

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

Nonparametric estimation of interaction functions for twotype pairwise interaction point processes is addressed. Such a problem is known to be challenging due to the intractable normalizing constant present in the density function. It is shown that the means of the marked interpoint distance functions embedded in the two-type pairwise interaction point process converge to the means of an inhomo...

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...

Bayesian Estimation of Shift Point in Shape Parameter of Inverse Gaussian Distribution Under Different Loss Functions

In this paper, a Bayesian approach is proposed for shift point detection in an inverse Gaussian distribution. In this study, the mean parameter of inverse Gaussian distribution is assumed to be constant and shift points in shape parameter is considered. First the posterior distribution of shape parameter is obtained. Then the Bayes estimators are derived under a class of priors and using variou...