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## Estimation of the killing rate parameter in a diffusion model

Horvat-Bokor, Roža; Huzak, Miljenko; Limić, Nedžad
Estimation of the killing rate parameter in a diffusion model // Mathematical communications, 17 (2012), 1; 171-185 (međunarodna recenzija, članak, znanstveni)

Naslov
Estimation of the killing rate parameter in a diffusion model

Autori
Horvat-Bokor, Roža ; Huzak, Miljenko ; Limić, Nedžad

Izvornik
Mathematical communications (1331-0623) 17 (2012), 1; 171-185

Ključne riječi
Diffusion with killing; censored data; minimum $\chi^2$-estimation; random search

Sažetak
We consider a parameter estimation problem for a diffusion with killing, starting at a point in an open and bounded set. The infinitesimal killing rate function depends on a control variable and parameters. Values of the control variable are known while parameters have unknown values which have to be estimated from data. The minimum of three times: the maximum observation time, the first exit time from the open set, and the killing time, is observed. Instead of the maximum likelihood estimation method we propose and use the minimum $\chi^2$-estimation method that is based on the conditional mean of the data observed before the maximum observation time is reached, and on the frequency of data that are equal to the maximum observation time. We prove that the estimator exists and is consistent and asymptotically normal. The method is illustrated by an example.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Projekt / tema
037-0372790-2800 - Statistička analiza slučajnih modela i primjene (Miljenko Huzak, )
037058
037-1193086-2771 - Numeričke metode u geofizičkim modelima (Saša Singer, )

Ustanove
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb

#### Časopis indeksira:

• Web of Science Core Collection (WoSCC)
• Science Citation Index Expanded (SCI-EXP)
• SCI-EXP, SSCI i/ili A&HCI
• Scopus

#### Uključenost u ostale bibliografske baze podataka:

• INSPEC
• MathSciNet
• Zentrallblatt für Mathematik/Mathematical Abstracts
• Current Index to Statistics