| The estimation of the intensity function of an in-homogeneous Poisson process is considered when the observable data consists of sampled shot noise that results from passing the Poisson process through an unknown linear time-invariant system. The proposed method consists of rst estimating a histogram of the underlying point process. The estimated his-togram is used to construct a kernel estim...

Let W be the number of points in (0, t] of a stationary finitestate Markov renewal point process. We derive a bound for the total variation distance between the distribution of W and a compound Poisson distribution. For any nonnegative random variable ζ, we construct a “strong memoryless time” ζ̂ such that ζ − t is exponentially distributed conditional on {ζ̂ ≤ t, ζ > t}, for each t. This is used...

Adaptive choice of smoothing parameters for nonparametric Poisson regression (O’Sullivan et. al., 1986) is considered in this paper. A computable approximation of the unbiased risk estimate (AUBR) for Poisson regression is introduced. This approximation can be used to automatically tune the smoothing parameter for the penalized likelihood estimator. An alternative choice is the generalized appr...

Maoist insurgency is considered as the single largest internal security challenge ever faced by India since its independence. Our initial analysis showed that the intensity of Maoist insurgency was high in those districts of Chattishgarh where both the education and income index components of human development index were low. This analysis concur with recent UNESCO report “Education under attac...

The a.s. connectivity of the Euclidean minimal spanning forest MSF(X) on a homogeneous Poisson point process X ⊂ R is an open problem for dimension d > 2. We introduce a descending family of graphs (Gn)n≥2 that can be seen as approximations to the MSF in the sense that MSF(X) = ⋂∞ n=2Gn(X). For n = 2 one recovers the relative neighborhood graph or, in other words, the β-skeleton with β = 2. We ...