likelihoodNormalestimfix function

Likelihood Function When The Fixed Effect Is Estimated

Computation of -2 loglikelihood of the mixed SDE with Normal distribution of the random effects when the fixed effect is estimated for random 1 or 2 $dXj(t)= (\alpha_j- \beta_j Xj(t))dt + \sigma a(Xj(t)) dWj(t)$.

likelihoodNormalestimfix(mu1, mu2, omega, U, V, estimphi, random)

Arguments

• mu1: current value of the mean of the first effect
• mu2: current value of the mean of the second effect
• 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.

Returns

• 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