A J–function for inhomogeneous point processes

We propose new summary statistics for intensity‐reweighted moment stationary point processes, that is, point processes with translation invariant n‐point correlation functions for all , that generalise the well known J‐, empty space, and spherical Palm contact distribution functions. We represent these statistics in terms of generating functionals and relate the inhomogeneous J‐function to the inhomogeneous reduced second moment function. Extensions to space time and marked point processes are briefly discussed.     

Estimation and testing of crossing‐points in fixed design regression

Many phenomena in the life sciences can be analyzed by using a fixed design regression model with a regression function m that exhibits a crossing‐point in the following sense: the regression function runs below or above its mean level, respectively, according as the input variable lies to the left or to the right of that crossing‐point, or vice versa. We propose a non‐parametric estimator and show weak and strong consistency as long as the crossing‐point is unique. It is defined as maximizing point arg max of a certain marked empirical process. For testing the hypothesis H₀ that the regression function m actually is constant (no crossing‐point), a decision rule is designed for the specific alternative H₁ that m possesses a crossing‐point. The pertaining test‐statistic is the ratio max/argmax of the maximum value and the maximizing point of the marked empirical process. Under the hypothesis the ratio converges in distribution to the corresponding ratio of a reflected Brownian bridge, for which we derive the distribution function. The test is consistent on the whole alternative and superior to the corresponding Kolmogorov–Smirnov test, which is based only on the maximal value max. Some practical examples of possible applications are given where a certain study about dental phobia is discussed in more detail.     

Trivariate non‐Gaussian copulas to analyze the spatial behavior of rat sightings

The brown rat lives with man in a wide variety of environmental contexts and adversely affects public health by transmission of diseases, bites, and allergies. Understanding behavioral and spatial correlation aspects of pest species can contribute to their effective management and control. Rat sightings can be described by spatial coordinates in a particular region of interest defining a spatial point pattern. In this paper, we investigate the spatial structure of rat sightings in the Latina district of Madrid (Spain) and its relation to a number of distance‐based covariates that relate to the proliferation of rats. Given a number of locations, biologically considered as attractor points, the spatial dependence is modeled by distance‐based covariates and angular orientations through copula functions. We build a particular spatial trivariate distribution using univariate margins coming from the covariate information and provide predictive distributions for such distances and angular orientations.     

Aspects of second‐order analysis of structured inhomogeneous spatio‐temporal point processes

Statistical methodology for spatio‐temporal point processes is in its infancy. We consider second‐order analysis based on pair correlation functions and K‐functions for general inhomogeneous spatio‐temporal point processes and for inhomogeneous spatio‐temporal Cox processes. Assuming spatio‐temporal separability of the intensity function, we clarify different meanings of second‐order spatio‐temporal separability. One is second‐order spatio‐temporal independence and relates to log‐Gaussian Cox processes with an additive covariance structure of the underlying spatio‐temporal Gaussian process. Another concerns shot‐noise Cox processes with a separable spatio‐temporal covariance density. We propose diagnostic procedures for checking hypotheses of second‐order spatio‐temporal separability, which we apply on simulated and real data.     

Evaluation of critical constructs for measurement of sustainable supply chain practices in lean‐agile firms of Indian origin: A hybrid ISM‐ANP approach

The purpose of this paper is to evaluate the critical criteria that are influencing the successful implementation of sustainable supply chain practices (SSCP) in the lean‐agile manufacturing firm. From the systematic literature review and field professionals' opinion, various criteria that are influencing sustainable supply chain were identified. Data were collected from 16 experts and analysed by an integrated approach of “interpretive structural modeling (ISM) and analytic network process (ANP).” ISM methodology was utilized to get a hierarchical relationship between all criteria. Further, the input to the ANP matrices was taken from the output of ISM, and three organizations that differ in their principle of operation were ranked to find out the extent of implementation of SSCP in the Indian context. The obtained results indicate that “Information technology‐enabled system support (ITS), SC member's awareness and literacy (SAL), Societal issues (SIS), and Scarcity of natural resources (SNR)” were most significant constructs for successful implementation of SSCP for the case organizations.