likelihoodNormal {mixedsde}

Computation Of The Log Likelihood In Mixed Stochastic Differential Equations

Description

Computation of -2 loglikelihood of the mixed SDE with Normal distribution of the random effects dXj(t)= (\alpha_j- \beta_j Xj(t))dt + \sigma a(Xj(t)) dWj(t).

Usage

likelihoodNormal(mu, omega, U, V, estimphi, random)

Arguments

mu

current value of the mean of the normal distribution

omega

current value of the standard deviation of the normal distribution

U

vector of the M sufficient statistics U (see UV)

V

vector of the M sufficient statistics V (see UV)

estimphi

vector or matrix of estimators of the random effects

random

random effects in the drift: 1 if one additive random effect, 2 if one multiplicative random effect or c(1,2) if 2 random effects.

Value

L

value of -2 x loglikelihood

References

Maximum likelihood estimation for stochastic differential equations with random effects, M. Delattre, V. Genon-Catalot and A. Samson, Scandinavian Journal of Statistics 2012, Vol 40, 322–343