A cautionary note on the variance of empirical pair correlation function

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10434768" target="_blank" >RIV/00216208:11320/21:10434768 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=S-1Ummou64" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=S-1Ummou64</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/sta4.406" target="_blank" >10.1002/sta4.406</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A cautionary note on the variance of empirical pair correlation function

Popis výsledku v původním jazyce

Point processes are popular models for data consisting of a random configuration of points, such as positions of trees of a given species in a forest stand, locations of earthquakes&apos; epicentres or positions of proteins in a cell membrane. Pair correlation function is a functional summary characteristic quantifying the interactions between pairs of points of the process at different distances. In practice, kernel estimators of the pair correlation function are mostly used, which require the user to choose the bandwidth of the smoothing kernel. When looking for the optimal bandwidth, higher order terms of the variance of the estimator are often neglected. We present the detailed formulas for the variance and argue that the higher order terms contribute the most to the variance and should not be ignored. Furthermore, we adapt a well-known variance approximation formula to accommodate the popular translation edge correction factor. We compare the original and the adjusted approximation formula to the exact variance obtained by numerical integration and to the empirical variance obtained from simulated realizations. We conclude that the variance approximations do not perform well and that modern cross-validation approaches to bandwidth selection should be preferred in practice.

Název v anglickém jazyce

A cautionary note on the variance of empirical pair correlation function

Popis výsledku anglicky

Point processes are popular models for data consisting of a random configuration of points, such as positions of trees of a given species in a forest stand, locations of earthquakes&apos; epicentres or positions of proteins in a cell membrane. Pair correlation function is a functional summary characteristic quantifying the interactions between pairs of points of the process at different distances. In practice, kernel estimators of the pair correlation function are mostly used, which require the user to choose the bandwidth of the smoothing kernel. When looking for the optimal bandwidth, higher order terms of the variance of the estimator are often neglected. We present the detailed formulas for the variance and argue that the higher order terms contribute the most to the variance and should not be ignored. Furthermore, we adapt a well-known variance approximation formula to accommodate the popular translation edge correction factor. We compare the original and the adjusted approximation formula to the exact variance obtained by numerical integration and to the empirical variance obtained from simulated realizations. We conclude that the variance approximations do not perform well and that modern cross-validation approaches to bandwidth selection should be preferred in practice.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/GA19-04412S" target="_blank" >GA19-04412S: Nové přístupy k modelování a statistice náhodných množin</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Stat [online]

ISSN

2049-1573

e-ISSN

—

Svazek periodika

10

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

12

Strana od-do

e406

Kód UT WoS článku

000680940600001

EID výsledku v databázi Scopus

2-s2.0-85121761640