Nonparametric analysis of earthquake point-process data

Choi, Edwin; Hall, Peter

doi:10.1214/lnms/1215090076

Cited by 7 publications

(4 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although parametric models are widely used, their estimation has many disadvantages, often related to the definition of a reliable mathematical model from the geophysical theory (Choi and Hall 2001) and to the sensitivity of statistical estimates to the composition of the space-time region under study (Choi and Hall 2001).…”

Section: Etas Model a Particular Branching Point Processmentioning

confidence: 99%

Alternated estimation in semi-parametric space-time branching-type point processes with application to seismic catalogs

Adelfio

Chiodi

2014

Stoch Environ Res Risk Assess

View full text Add to dashboard Cite

An estimation approach for the semi-parametric intensity function of a class of space-time point processes is introduced. In particular we want to account for the estimation of parametric and nonparametric components simultaneously, applying a forward predictive likelihood to semi-parametric models. For each event, the probability of being a background event or an offspring is therefore estimated.

show abstract

Section: Etas Model a Particular Branching Point Processmentioning

confidence: 99%

Alternated estimation in semi-parametric space-time branching-type point processes with application to seismic catalogs

Adelfio

Chiodi

2014

Stoch Environ Res Risk Assess

View full text Add to dashboard Cite

show abstract

“…We also created versions of the relative risk functions with changes to the level of risk variation, with low and high variation instances for each example. The control density in each case was defined by a fixed-bandwidth kernel density estimate calculated from the observed control data, sharpened using Choi and Hall's method 34 to avoid too much blurring of detail in areas of high density. The corresponding (synthetic) case density was then derived using (1).…”

Section: Numerical Studiesmentioning

confidence: 99%

Shrinkage estimators of the spatial relative risk function

Hazelton

2023

Statistics in Medicine

View full text Add to dashboard Cite

The spatial relative risk function describes differences in the geographical distribution of two types of points, such as locations of cases and controls in an epidemiological study. It is defined as the ratio of the two underlying densities. Estimation of spatial relative risk is typically done using kernel estimates of these densities, but this procedure is often challenging in practice because of the high degree of spatial inhomogeneity in the distributions. This makes it difficult to obtain estimates of the relative risk that are stable in areas of sparse data while retaining necessary detail elsewhere, and consequently difficult to distinguish true risk hotspots from stochastic bumps in the risk function. We study shrinkage estimators of the spatial relative risk function to address these problems. In particular, we propose a new lasso‐type estimator that shrinks a standard kernel estimator of the log‐relative risk function towards zero. The shrinkage tuning parameter can be adjusted to help quantify the degree of evidence for the existence of risk hotspots, or selected to optimize a cross‐validation criterion. The performance of the lasso estimator is encouraging both on a simulation study and on real‐world examples.

show abstract

“…Although parametric models are widely used, their estimation has many disadvantages, often related to the definition of a reliable mathematical model from the geophysical theory (Choi and Hall, 1999) and to the sensitivity of statistical estimates to the composition of the space-time region under study (Choi and Hall, 2001).…”

Section: Application: Kernel Estimators For Seismic Processesmentioning

confidence: 99%

Forward likelihood‐based predictive approach for space–time point processes

Chiodi

Adelfio

2011

Environmetrics

View full text Add to dashboard Cite

Dealing with data from a space-time point process, the estimation of the conditional intensity function is a crucial issue even if a complete definition of a parametric model is not available. In particular, in case of exploratory contexts or if we want to assess the adequacy of a specific parametric model, some kind of nonparametric estimation procedure could be useful.Often, for these purposes kernel estimators are used and the estimation of the intensity function depends on the estimation of bandwidth parameters. In some fields, like for instance the seismological one, predictive properties of the estimated intensity function are pursued. Since a direct ML approach cannot be used, we propose an estimation procedure based on the subsequent increments of likelihood obtained adding an observation one at a time. Simulated results and some applications to statistical seismology are provided.

show abstract

Nonparametric analysis of earthquake point-process data

Cited by 7 publications

References 18 publications

Alternated estimation in semi-parametric space-time branching-type point processes with application to seismic catalogs

Alternated estimation in semi-parametric space-time branching-type point processes with application to seismic catalogs

Shrinkage estimators of the spatial relative risk function

Forward likelihood‐based predictive approach for space–time point processes

Contact Info

Product

Resources

About