snr | R Documentation |
Calculate self-normalized residuals based on the Gaussian quasi-likelihood estimator.
snr(yuima, start, lower, upper, withdrift)
yuima |
a yuima object. |
lower |
a named list for specifying lower bounds of parameters. |
upper |
a named list for specifying upper bounds of parameters. |
start |
initial values to be passed to the optimizer. |
withdrift |
use drift information for constructing self-normalized residuals. by default, withdrift = FALSE |
This function calculates the Gaussian quasi maximum likelihood estimator and associated self-normalized residuals.
estimator |
Gaussian quasi maximum likelihood estimator |
snr |
self-normalized residuals based on the Gaussian quasi maximum likelihood estimator |
The YUIMA Project Team
Contacts: Yuma Uehara y-uehara@ism.ac.jp
Masuda, H. (2013). Asymptotics for functionals of self-normalized residuals of discretely observed stochastic processes. Stochastic Processes and their Applications 123 (2013), 2752–2778
## Not run: # Test code (1. diffusion case) yuima.mod <- setModel(drift="-theta*x",diffusion="theta1/sqrt(1+x^2)") n <- 10000 ysamp <- setSampling(Terminal=n^(1/3),n=n) yuima <- setYuima(model=yuima.mod, sampling=ysamp) set.seed(123) yuima <- simulate(yuima, xinit=0, true.parameter = list(theta=2,theta1=3)) start=list(theta=3,theta1=0.5) lower=list(theta=1,theta1=0.3) upper=list(theta=5,theta1=3) res <- snr(yuima,start,lower,upper) str(res) # Test code (2.jump diffusion case) a<-3 b<-5 mod <- setModel(drift="10-theta*x", #drift="10-3*x/(1+x^2)", diffusion="theta1*(2+x^2)/(1+x^2)", jump.coeff="1", # measure=list(intensity="10",df=list("dgamma(z, a, b)")), measure=list(intensity="10",df=list("dunif(z, a, b)")), measure.type="CP") T <- 100 ## Terminal n <- 10000 ## generation size samp <- setSampling(Terminal=T, n=n) ## define sampling scheme yuima <- setYuima(model = mod, sampling = samp) yuima <- simulate(yuima, xinit=1, true.parameter=list(theta=2,theta1=sqrt(2),a=a,b=b), sampling = samp) start=list(theta=3,theta1=0.5) lower=list(theta=1,theta1=0.3) upper=list(theta=5,theta1=3) res <- snr(yuima,start,lower,upper) str(res) ## End(Not run)
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