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Marked Point Processes (marked + point_process)

Distribution by Scientific Domains

Mathematics and Statistics	66%
Business, Economics, Finance and Accounting	33%

Selected Abstracts

Moment estimation for statistics from marked point processes

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2001
Dimitris N. Politis
In spatial statistics the data typically consist of measurements of some quantity at irregularly scattered locations; in other words, the data form a realization of a marked point process. In this paper, we formulate subsampling estimators of the moments of general statistics computed from marked point process data, and we establish their L2 -consistency. The variance estimator in particular can be used for the construction of confidence intervals for estimated parameters. A practical data-based method for choosing a subsampling parameter is given and illustrated on a data set. Finite sample simulation examples are also presented. [source]

Cluster Pattern Detection in Spatial Data Based on Monte Carlo Inference

BIOMETRICAL JOURNAL, Issue 4 2007
Radu Stefan Stoica
Abstract Clusters in a data point field exhibit spatially specified regions in the observation window. The method proposed in this paper addresses the cluster detection problem from the perspective of detection of these spatial regions. These regions are supposed to be formed of overlapping random disks driven by a marked point process. The distribution of such a process has two components. The first is related to the location of the disks in the field of observation and is defined as an inhomogeneous Poisson process. The second one is related to the interaction between disks and is constructed by the superposition of an area-interaction and a pairwise interaction processes. The model is applied on spatial data coming from animal epidemiology. The proposed method tackles several aspects related to cluster pattern detection: heterogeneity of data, smoothing effects, statistical descriptors, probability of cluster presence, testing for the cluster presence. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

The Econometrics of Ultra-high-frequency Data

ECONOMETRICA, Issue 1 2000
Robert F. Engle
Ultra-high-frequency data is defined to be a full record of transactions and their associated characteristics. The transaction arrival times and accompanying measures can be analyzed as marked point processes. The ACD point process developed by Engle and Russell (1998) is applied to IBM transactions arrival times to develop semiparametric hazard estimates and conditional intensities. Combining these intensities with a GARCH model of prices produces ultra-high-frequency measures of volatility. Both returns and variances are found to be negatively influenced by long durations as suggested by asymmetric information models of market micro-structure. [source]

Spatial,temporal marked point processes: a spectrum of stochastic models

ENVIRONMETRICS, Issue 3-4 2010
Eric Renshaw
Abstract Many processes that develop through space and time do so in response not only to their own individual growth mechanisms but also in response to interactive pressures induced by their neighbours. The growth of trees in a forest which compete for light and nutrient resources, for example, provides a classic illustration of this general spatial,temporal growth-interaction process. Not only has its mathematical representation proved to be a powerful tool in the study and analysis of marked point patterns since it may easily be simulated, but it has also been shown to be highly flexible in terms of its application since it is robust with respect to incorrect choice of model selection. Moreover, it is highly amenable to maximum likelihood and least squares parameter estimation techniques. Currently the algorithm comprises deterministic growth and interaction coupled with a stochastic arrival and departure mechanism. So for systems with a fixed number of particles there is an inherent lack of randomness. A variety of different stochastic approaches are therefore presented, from the exact event,time model through to the associated stochastic differential equation, taking in time-increment and Tau- and Langevin-Leaping approximations en route. The main algorithm is illustrated through application to forest management and high-intensity packing of hard particle systems, and comparisons are made with the established force biased approach. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Moment estimation for statistics from marked point processes

The Term Structure of Simple Forward Rates with Jump Risk

MATHEMATICAL FINANCE, Issue 3 2003
Paul Glasserman
This paper characterizes the arbitrage-free dynamics of interest rates, in the presence of both jumps and diffusion, when the term structure is modeled through simple forward rates (i.e., through discretely compounded forward rates evolving continuously in time) or forward swap rates. Whereas instantaneous continuously compounded rates form the basis of most traditional interest rate models, simply compounded rates and their parameters are more directly observable in practice and are the basis of recent research on "market models." We consider very general types of jump processes, modeled through marked point processes, allowing randomness in jump sizes and dependence between jump sizes, jump times, and interest rates. We make explicit how jump and diffusion risk premia enter into the dynamics of simple forward rates. We also formulate reasonably tractable subclasses of models and provide pricing formulas for some derivative securities, including interest rate caps and options on swaps. Through these formulas, we illustrate the effect of jumps on implied volatilities in interest rate derivatives. [source]