TY - JOUR
T1 - Nonparametric and parametric estimation for a linear germination-growth model
AU - Chiu, S. N.
AU - Quine, M. P.
AU - Stewart, M.
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2000/9
Y1 - 2000/9
N2 - Seeds are planted on the interval [0, L] at various locations. Each seed has a location x and a potential germination time t ε [0, ∞), and it is assumed that the collection of such (x, t) pairs forms a Poisson process in [0, L] x [0, ∞) with intensity measure dxdΛ(t). From each seed that germinates, an inhibiting region grows bidirectionally at rate 2v. These regions inhibit germination of any seed in the region with a later potential germination time. Thus, seeds only germinate in the uninhibited part of [0, L]. We want to estimate A on the basis of one or more realizations of the process, the data being the locations and germination times of the germinated seeds. We derive the maximum likelihood estimator of v and a nonparametric estimator of A and describe methods of obtaining parametric estimates from it, illustrating these with reference to gamma densities. Simulation results are described and the methods applied to some neurobiological data. An Appendix outlines the S-PLUS code used.
AB - Seeds are planted on the interval [0, L] at various locations. Each seed has a location x and a potential germination time t ε [0, ∞), and it is assumed that the collection of such (x, t) pairs forms a Poisson process in [0, L] x [0, ∞) with intensity measure dxdΛ(t). From each seed that germinates, an inhibiting region grows bidirectionally at rate 2v. These regions inhibit germination of any seed in the region with a later potential germination time. Thus, seeds only germinate in the uninhibited part of [0, L]. We want to estimate A on the basis of one or more realizations of the process, the data being the locations and germination times of the germinated seeds. We derive the maximum likelihood estimator of v and a nonparametric estimator of A and describe methods of obtaining parametric estimates from it, illustrating these with reference to gamma densities. Simulation results are described and the methods applied to some neurobiological data. An Appendix outlines the S-PLUS code used.
KW - Boolean model
KW - DNA replication
KW - Germination-growth process
KW - Inhibition
KW - Maximum likelihood estimation
KW - Nucleation
KW - Synaptic transmission
UR - http://www.scopus.com/inward/record.url?scp=0033857558&partnerID=8YFLogxK
U2 - 10.1111/j.0006-341X.2000.00755.x
DO - 10.1111/j.0006-341X.2000.00755.x
M3 - Journal article
C2 - 10985212
AN - SCOPUS:0033857558
SN - 0006-341X
VL - 56
SP - 755
EP - 760
JO - Biometrics
JF - Biometrics
IS - 3
ER -